diff --git "a/9dAzT4oBgHgl3EQfgvzi/content/tmp_files/load_file.txt" "b/9dAzT4oBgHgl3EQfgvzi/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/9dAzT4oBgHgl3EQfgvzi/content/tmp_files/load_file.txt" @@ -0,0 +1,853 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf,len=852 +page_content='Dynamic Response of Wigner Crystals Lili Zhao, Wenlu Lin, and Yang Liu∗ International Center for Quantum Materials, Peking University, Haidian, Beijing 100871, China Yoon Jang Chung, Adbhut Gupta, Kirk W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Baldwin, and Loren N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Pfeiffer Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA The Wigner crystal, an ordered array of electrons, is one of the very first proposed many-body phases stabilized by the electron-electron interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' This electron solid phase has been reported in ultra-clean two-dimensional electron systems at extremely low temperatures, where the Coulomb interaction dominants over the kinetic energy, disorder potential and thermal fluctuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We closely examine this quantum phase with capacitance measurements where the device length-scale is com- parable with the crystal’s correlation length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The extraordinarily high performance of our technique makes it possible to quantitatively study the dynamic response of the Wigner crystal within the single crystal regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Our result will greatly boost the study of this inscrutable electron solid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Interacting two-dimensional electron system (2DES) subjected to high perpendicular magnetic fields (B) and cooled to low temperatures exhibits a plethora of exotic states [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The Wigner crystal (WC) [2] terminates the sequence of fractional quantum Hall states at very small landau level filling factor [3–24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' This electron solid is pinned by the ubiquitous residual disorder, manifests as an insulating phase in DC transport [3–11], and the elec- trons’ collective motion is evidenced by a resonance in AC transport [12–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' A series of experiments have been applied to investigate this correlated solid, such as the nonlinear I − V response [4, 16], the noise spectrum [5], the huge dielectric constant [20], the weak screening effi- ciency [21], the melting process [21–23], the nuclear mag- netic resonance [24] and the optics [25, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Capacitance measurements have revealed a series of quantum phenomena [21, 27–38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' In this work, we ex- amine the WC formed in an ultra-high mobility 2DES at ν <∼ 1/5 using high-precision capacitance measure- ment [39, 40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We find an exceedingly large capacitance at low measurement frequency f while the conductance is almost zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' This phenomenon is inconsistent with transporting electrons, but rather an evidence that the synchronous vibration of electrons induces a polarization current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' When we increase f, our high-precision mea- surement captures the fine structure of the resonance re- sponse with a puzzling ”half-dome” structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Our sys- tematic, quantitative results provide an in-depth insight of this murky quantum phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Our sample consists an ultra-clean low-density 2DES confined in a 70-nm-wide GaAs quantum well with elec- tron density n ≃ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='4 × 1010 cm−2 and mobility µ ≃ 17 ×106 cm2/(V·s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Each device has a pair of front concen- tric gates G1 and G2, whose outer and inner radius are r1 and r2, respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' see the inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 1(a) [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We study four devices with r1 =60 µm and r2 = 60, 80, 100 and 140 µm, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We measure the capacitance C and conductance G between the two gates using a cryo- genic bridge and analyze its output with a custom-made radio-frequency lock-in amplifier [39–41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 1(a) shows the C and G measured from the r1 = r2 = 60 µm sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Both C and G decrease as we increase the magnetic field B, owing to the mag- netic localization where the 2DES conductance σ ∝ (ne2τ)/m⋆(1+ω2 cτ 2), m⋆, ωc and τ are the effective mass, cyclotron frequency and transport scattering time of the electrons, respectively [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The C and G are finite at ν = 1/2 and 1/4 where the 2DES forms compressible composite Fermion Fermi sea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' When ν is an integer or a certain fraction such as 1/3 and 1/5, the 2DES forms incompressible quantum Hall liquids so that both C and G vanish [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' In all the above cases, the current is carried by trans- porting electrons, so that C has a positive dependence on G, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' C ∝ G3/2, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 1(b) [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Such a correlation discontinues when the WC forms at very low filling factors ν <∼ 1/5, see the blue shaded regions of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The vanishing conductance G suggests that the electrons are immovable, however, the surprisingly large capacitance C evidences that the WC hosts a cur- rent even surpassing the conducting Fermi sea at ν = 1/2 and 1/4 at much lower magnetic field!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The phase tran- sition between the WC and the liquid states are clearly evidenced by spikes in G (marked by solid circles in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 1(a)) and sharp raises in C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' A developing minimum is seen in G at 1/5 < ν < 2/9 (marked by the up-arrow) when C has a peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' This G minimum develops towards zero and the C peak saturates when the solid phase is stronger (see black traces in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 3(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' This is consistent with the reentrant insulating phase [3–5, 16, 19, 43, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' It is important to mention that the 2DES in our de- vices is effectively “isolated” and we are merely transfer- ring charges between different regions within one quan- tum phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Similar to the dielectric materials which also have no transporting electrons, the collective motion of all electrons, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' the k → 0 phonon mode of WC, can generate polarization charges and corresponding polar- ization current in response to the in-plane component of applied electric field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' An infinitesimally small but ubiquitous disorder pins the WC so that electrons can arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='01475v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='mes-hall] 4 Jan 2023 2 0 2 4 6 8 10 12 14 B (T) 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='4 C (pF) 1 0 G (µS) ν=1 1 3 1 4 1 2 1 5 2 9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 C (pF) 0 1 G3/2 (µS3/2) WC Liquid (b) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='0 ν(∝1/B) C (pF) (d) f=7 MHz T=30 mK r2=100 µm 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='4 ln(r2/r1) 8 4 0 1/CWC (1/pF) 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='5 T (e) 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='0 T lB (c) a0 x CWC 2DES E G2 G1 << << Q ∝ e-d/ζ d 0 h r1=r2=60 µm f=7 MHz T=30 mK (a) G2 G1 Al2O3 2DES r1 r2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (color online) (a) C and G measured from the r1 = r2 = 60 µm sample with 7 MHz excitation at 30 mK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The horizontal dashed lines represent the zeros of C or G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The blue shaded regions mark the presence of WC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Inset is the cartoon of our device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (b) The correlation between C and G in panel (a) data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Transporting current dominates at B < 8 T where C ∝ G3/2, indicated the red solid line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' When the WC polarization current dominates, C ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 pF and G is about zero (the blue box).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (c) The schematic model describing the collective motion of electrons in the pinned WC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' h is the depth of 2DES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The equally spaced (by the lattice constant a0) vertical bars represent the equilibrium position of electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The gray-scaled solid circles represent the electron position at finite external electric field E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The darker gray corresponds to larger electron displacement x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The radius of individual electron is about the magnetic length lB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The accumulated charge Q is proportional to ∇ · x, and decays exponentially as a function of the distance d from the gate boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' ζ is the decay length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' CWC is the effective capacitance of WC in the un-gated region between the two gates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (d) C v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' ν of the r2=100 µm sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The black dashed line is the zero of C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The red dashed line is the linear extension of data, showing that C = 0 at the extreme quantum limit ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (e) 1/CWC v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' ln(r2/r1) at two different magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' only be driven out of their equilibrium lattice site by a small displacement x, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 1(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Dur- ing the experiments, we use excitation Vin ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='1 mVrms and the measured WC capacitance is ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='15 pF at 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='5 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The polarization charge accumulated under the inner gate is Q = CVin ∼ 100 e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The corresponding elec- tron displacement at the boundary of the inner gate, |x(r1)| ≃ Q/(2πr1ne) ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='6 nm, is much smaller than the magnetic length lB = � ¯h/eB ∼ 8 nm, substanti- ating our assumption that the electrons vibrate diminu- tively around their equilibrium lattice sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' An ideal, disorder-free WC is effectively a perfect di- electric with infinite permittivity, so that the device ca- pacitance should be close to its zero-field value C0 ∼ 1 pF when 2DES is an excellent conductor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We note that C0 is consistent with the device geometry, ϵ0ϵGaAsπr2 1/h ≃ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='3 pF, where ϵGaAs = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='8 is the relative dielectric constant of GaAs and h ≃ 960 nm is the depth of 2DES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' How- ever, the measured C ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='15 pF in the WC regime is much smaller than C0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' This discrepancy is likely caused by the friction-like disorder which poses a pinning force ≃ −βx on the electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' When the crystal’s inversion symmetry is broken, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' x is non-uniform and J (x) is finite, the electron-electron interaction generates a restor- ing force ≃ −a0µijJ (x), where µij, a0 and J (x) are the elastic tensor, WC lattice constant and the Jacobi ma- trix of x, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' At the low frequency limit, the WC is always at equilibrium and all forces are balanced, eE − a0µijJ (x) − βx = 0, E is the total parallel electric field on the WC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' E is approximately zero under the metal gates, since the gate-to-2DES distance h is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Therefore, x de- creases exponentially when the distance from the gate boundary d increases, x ∝ exp(−d/ζ), where ζ = µa0/β is the decay length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Deeply inside the gates, electrons feel neither parallel electric field nor net pressure from nearby electrons, so that their displacement x remains approximately zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' This region does not contribute to the capacitive response, and the effective gate area re- duces to about 2πr1ζ and 2πr2ζ at the inner and outer gate, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Because r1 = r2 = 60 µm in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 1(a), the experimentally measured C ≈ ϵ0ϵGaAs/h · 2πr1ζ/2 ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='15 pF at 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='5 T corresponds to a decay length ζ ≃ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='7 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Interestingly, our result shows a linear dependence C ∝ 1/B in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 1(d), suggesting that β ∝ l−2 B if we assume µij is independent on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Especially, the pinning becomes infinitely strong, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' β → ∞, at the extreme quantum limit lB → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 3 The permittivity of a disorder-pinned WC is no longer infinitely large, since a non-zero electric field E is neces- sary to sustain a finite x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' If we assume x is a constant in the ring area between the two gates, so that eE = βx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The residual E can be modeled as a serial capacitance CWC ≈ 2πne2/β · [ln(r2/r1)]−1 in our device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We then measure different devices with r1= 60 µm and r2 = 60, 80, 100 and 140 µm, and calculate the corresponding CWC through C−1 WC = C−1 −(r1 +r2)/r2 ·C−1 r1=r2, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 1(e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' By fitting the linear dependence C−1 WC ∝ ln(r2/r1), we estimate the pinning strength β to be about 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='3 ×10−9 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='1 ×10−9 N/m at B = 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='5 and 12 T, respectively [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Finally, assuming µij ≈ µ · δij, we can estimate the WC elastic modulus µ ≈ β · ζ/a0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' For example, µ is about 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='6 × 10−7 N/m at 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='5 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='22 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 C (pF) 2 0 G (μS) ν 30 mK 95 mK 110 mK 125 mK 145 mK 200 mK 1/5 2/11 1/7 (a) 0 100 200 T (mK) 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 C (pF) ν=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='18 ν=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='14 2 0 G (μS) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='20 ν 0 200 TC (mK) FQH liquid WC Compressible liquid (b) TC TC r2=80 μm f=17 MHz FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (color online) (a) C and G vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' ν measured at vari- ous temperatures from the r2 = 80 µm sample with 17 MHz excitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (b) Summarized C and G vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' T at ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='14 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='18 from the panel (a) data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' A critical temperature Tc at certain ν is defined either as the temperature when G has a peak at ν in panel (a) or as the temperature when G vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' T trace reaches maximum in panel (b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' marked by the black and red arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The panel (b) inset summarizes the Tc us- ing the two equivalent definitions using black and red circles, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The diagram can be separated into three differ- ent regions corresponding to the WC, the fractional quantum Hall (FQH) liquid and the compressible liquid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 2 reveals an intriguing temperature-induced solid- liquid phase transition when the WC melts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 2(a) shows C and G taken from the r2 = 80 µm sample at various temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' At a certain temperature, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' at T ≈ 110 mK, C ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 pF when the 2DES forms WC at ν <∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='16 and vanishes when it is a liquid phase at ν >∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' G has a peak at ν ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='175 when C vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' ν has the maximal negative slope, and it is small when the 2DES is either a WC at ν < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='17 or a liquid at ν > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='19 [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' At very high temperature T >∼ 200 mK, both C and G are close to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 2(b), we summarized C and G as a function of T at two different filling factors to bet- ter illustrate this solid-liquid transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' At ν ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='14, for example, C is large and G is small at T <∼ 100 mK when the WC is stable [47], while both of them become small at T >∼ 200 mK when the 2DES is a liquid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The G has a peak at a critical temperature TC, marked by the red arrows, around which the precipitous decrease of C hap- pens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Alternatively, TC at a certain filling factor ν can be defined as the temperature when the G has a peak (black arrow in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 2(a)) at ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We summarize TC obtained us- ing these two equivalent procedures in the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 2(b) inset with corresponding red and black symbols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' TC has a lin- ear dependence on ν whose two intercepts are TC ≃ 340 mK at the extreme quantum limit ν = 0, and ν ≃ 1/4 at TC = 0 mK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 2(b) evolution can be qualitatively under- stood by the coexistence of transport and polarization currents at the solid-liquid transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The large C re- duces to almost zero when the transport current domi- nates over the polarization current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' G is a measure of the 2DES’s capacity to absorb and dissipate power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' It is negligible if either of these two currents dominates, since the polarization current is dissipation-less and the dissi- pating transport current is difficult to excite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' G becomes large when these two currents coexist nip and tuck at intermediate T when the excited polarization charge can be just dissipated by the transport current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The WC exhibits a resonance when we increase the excitation frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 3(a), the C and G measured from the r2 = 100 µm sample using different excitation frequencies change enormously when the WC presents (blue shaded region).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' G is almost zero and C is large at f ≃ 7 MHz, and G becomes finite and C becomes even larger at f ≃ 23 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' At slightly higher frequency 27 MHz, G reaches its maximum and C drops to about zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Further increasing f, G gradually declines while C first becomes negative at 35 MHz and then gradually approaches zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The summarized C and G vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' f at two certain fillings in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 3(b), resembles qualitatively a resonant behavior with resonance frequency fr ≃ 26 MHz (when C = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 3(c) studies this resonance at different temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The data is taken from the r2 ≃ 80 µm sample whose resonance frequency is about 35 MHz [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The abrupt change of C near fr becomes gradual and the G peak flattens at higher temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 4 10 0 G (μS) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='24 ν 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='4 0 C (pF) 7 23 27 35 77 r2=100 μm 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 ν=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='14 30 60 140 280 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 10 0 10 100 f (MHz) r2=80 μm 10 0 10 100 f (MHz) ν=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='14 ν=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='213 r2=100 μm T=30 mK T=30 mK (b) (a) (c) fr=35 MHz fr=26 MHz ν=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='213 f (MHz) T (mK) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (color online) (a) C and G vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' ν taken from the r2=100 µm sample using different excitation frequencies f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We see a violent change of C and G at different f in the blue region where the WC appears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (b) The C and G vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' f extracted from the panel (a) trace at ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='14 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='213.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The resonance frequency fr, defined as the frequency when C changes its sign, is about 26 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (c) The C and G vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' f at ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='14 and different temperatures, data taken from the r2=80 µm sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The resonance disappears at T ≃ 280 mK when C and G remain nearly zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Both C and G become flat zero at T >∼ 280 mK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' It is noteworthy that, as long as a resonance is seen, fr is nearly independent on the filling factor (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 3(b)) and temperatures (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 3(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' This is consistent with another experimental study using surface acoustic wave [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The resonance of WC is usually explained by the pinning mode [18, 49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The resonance frequency is related to the mean free path LT of the transverse phonon through LT = (2πµt,cl/neBfr)1/2, where µt,cl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='245e2n3/2/4πϵ0ϵGaAs is the classical shear modulus of WC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' fr = 26 MHz corresponds to LT ≃ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 µm, very similar to ζ ≃ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='7 µm in our Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 1(c) discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' This is justifiable because both LT and ζ describe the length-scale within which the collective motion of WC is damped/scattered by the random pinning potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Before ending the discussion, we would like to highlight the puzzling ”half-dome” structure of the resonance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' G has a regular-shaped resonance peak, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' G decreases gradually on both sides of fr, when either the WC is weak ( ν ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='213 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 3(b)) or the temperature is high (T ≃ 140 mK in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 3(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Surprisingly, the resonance peak becomes quite peculiar when the WC is strong at ν ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='14 and T ≃ 30 mK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' G gradually decreases from its peak at fr on the high frequency side f > fr, while it vanishes instantly when the frequency is lower than fr, resulting in a ”half-dome” G vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' f trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Meanwhile, the C increases by ∼ 2 times and then abruptly changes to negative at fr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' This anomalous ”half-dome” feature is seen in all of our devices as long as the WC is strong and temperature is sufficiently low, suggesting a threshold frequency for the power dissipation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' In conclusion, using the extraordinarily high-precision capacitance measurement technique, we investigate the dynamic response of WC systematically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' From the quan- titative results and using a simple model, we can study several physical properties of the WC such as elastic mod- ulus, dielectric constant, pinning strength, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=', and dis- cover a puzzling ”half-dome” feature in the resonance peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Our results certainly shine light on the study of WC and provides new insight on its dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We acknowledge support by the National Nature Sci- ence Foundation of China (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 92065104 and 12074010) and the National Basic Research Program of China (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 2019YFA0308403) for sample fabrica- tion and measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' This research is funded in part by the Gordon and Betty Moore Foundation’s EPiQS Initia- tive, Grant GBMF9615 to L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Pfeiffer, and by the Na- tional Science Foundation MRSEC grant DMR 2011750 to Princeton University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We thank L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Engel, Bo Yang and Xin Lin for valuable discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' ∗ liuyang02@pku.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='cn [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Jain, Composite Fermions (Cambridge University Press, Cambridge, UK, 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [2] E.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Tsui, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Shayegan, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 67, 1630 (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [6] 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Deville, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Glattli, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Williams, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Paris, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Etienne, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 60, 2765 (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [16] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Williams, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Wright, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Clark, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' An- drei, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Deville, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Glattli, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Probst, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Etienne, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Dorin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' T.' 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T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Sajoto, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Engel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Santos, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Shayegan, Solid State Communications 95, 619 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [21] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Deng, L.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Baldwin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Pfeiffer, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Liu, Chinese Physics Letters 39, 097301 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [41] See Supplemental Material for detailed description of our sample information and measurement techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [42] The zero of C and G can be defined either by extrapolat- ing their field dependence to B = ∞, or by their values at strong quantum hall states such as ν = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' These two approaches are consistent with each other and the dash lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 1(a) represent the deduced zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [43] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Shayegan, in High Magnetic Fields: Science and Tech- nology, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 3, edited by F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Herlach and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Miura (World Scientific, Singapore, 2006) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 31–60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [44] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Shayegan, in Perspectives in Quantum Hall Effects, edited by S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Sarma and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Pinczuk (Wiley, New York, 1998) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 343–383.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [45] Alternatively, CWC can be modeled as a cylinder ca- pacitor whose height equals the effective thickness of the 2DES, Z0 ≈ 45 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The WC dielectric constant is ϵWC = (2πϵ0Z0∂(C−1 WC)/∂ ln(r2/r1))−1 ≈ 2 × 104 at 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='5 T, consistent with previous reported value in ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [46] We observe developing minimum at ν = 1/7, 2/11 dur- ing the solid-liquid phase transition, signaling that the fractional quantum Hall state emerges [8, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [47] C vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' T has a slightly positive slope in the WC region, possibly due to the softening of disorder pinning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [48] fr has no obvious dependence with sample geometry, which is about 35, 35, 26 and 29 MHz for samples with r2 = 60, 80, 100, 140 µm, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [49] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Fogler and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Huse, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' B 62, 7553 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 6 SUPPLEMENTARY MATERIALS Samples The sample we studied is made from a GaAs/AlGaAs heterostructure wafer grown by molecular beam epitaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' A 70 nm-wide GaAs quantum well is bound by AlGaAs spacer-layers and δ-doped layers on each side, and locates h ≃ 960 nm below the sample surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The as-grown den- sity of the 2DES is n ≃ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='4×1010 cm−2, and its mobility at 300 mK is µ ≃ 17 ×106 cm2/(V·s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Our sample is a 2 mm × 2 mm square piece with four In/Sn contacts at each corner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The contacts are grounded through a re- sistor to avoid signal leaking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We evaporate concentric, Au/Ti front gate pair G1 and G2 using standard lift- off process, whose outer and inner radius is r1 and r2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We deposit a 20 nm thick Al2O3 layer be- tween the two gates to prevent them from shorting with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The four outer-gates are merged into one piece so that the area of the outer gate G2 is much larger than the inner gate G1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Capacitance Measurement Setup The capacitance and conductance response is mea- sured with a cryogenic bridge similar to refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [39, 40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The kernel of the bridge consists four devices, Rh, Rr, Cr and C, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' S1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' C is the capacitance of sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We change the value of Rh to reach the balance condition C Cr = Rh Rr .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (1) The bridge output Vout is minimum at the balance con- dition, from which we calculate the C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' This is the so-call “V-curve” procedure, see refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' [39, 40] for more informa- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' In order to expand the allowed bandwidth of the ex- citation frequency, we add an impedance match network to the input of the bridge, shown as the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' S1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Vext is the signal source with 50 Ω output impedance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Vext drives a signal splitter box (the red dashed box) located at the top of the dilution refrigerator through a ∼2 m- long semi-rigid coaxial cable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The box input is a 1:5 transformer in series with a 50 Ω resistor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The trans- former output drives two serial connected 50 Ω resistors differentially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The differential signals are transmitted to the cryogenic sample holder (the blue dotted box) by two rigid coaxial cables of ∼2 m length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Another pair of impedance matching 50 Ω resistors are added at the input of the cryogenic bridge, and the 360 Ω resistors are chosen by balancing the competition between the perfor- mance and heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The characteristic impedance of all coaxial cables in the work is 50 Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The low-frequency signals Vquasi-DC1 and Vquasi-DC2 used to measure the value of Rh and Rr, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='1 µF capacitors are used to separate the high-frequency excitation signals and the quasi-DC signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The output Vout is approximately Vout ∝ S · ( Rh 360 + Rh − C Cr Rr 360 + Rr ) · Vext.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (2) S can be obtain from the “V-curve” procedure by linear fitting the VX vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Rh/(360+Rh), as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' S1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' VX and VY are the orthogonal component of Vout, � VX = |Vout| · cos(θ), (3) VY = |Vout| · sin(θ), (4) where θ is the phase of Vout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' We can derive the value of C using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (2) and (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The new balance condition of the revised bridge is C Cr = Rh Rr 360 + Rr 360 + Rh , (5) where the VX = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Note that the capacitance C and the conductance G of sample lead to the orthogonal component VX and VY, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Therefore, the G can be obtained from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (2) and (4) by replacing C/Cr with G/2πfCr, where f is the excitation frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' S1(c) shows our calibration measurement using different excitation frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The data is almost flat from 7 to ∼100 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' The measured capacitance begins to decline slowly above ∼100 MHz, possibly due to the parasitic inductance of bonding wires.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' 7 Rh Rr Cr C Vin + Vin Vout 360 Ω 360 Ω 50 Ω 50 Ω 1:5 50 Ω 50 Ω 50 Ω 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='1 μF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='1 μF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='1 μF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='1 μF Vext Vquasi-DC1 Vquasi-DC2 COAX COAX (a) 40 40 0 V (μV) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='6 Rh/(Rh+360) Vx Vy (b) Cr= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='1 pF f= 7 MHz Rr= 50 Ω 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='2 C (pF) 10 100 f (MHz) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='5 pF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='3 pF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='1 pF (c) COAX FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (color online) (a) Circuit diagram of measurement bridge with 50 Ω impedance match networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (b) The VX and VY from a typical “V-curve” procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' C is about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content='25 pF from the balance condition Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'} +page_content=' (c) The calibration results, by measuring commercial capacitors with different frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dAzT4oBgHgl3EQfgvzi/content/2301.01475v1.pdf'}