diff --git "a/09E4T4oBgHgl3EQfzA3P/content/tmp_files/load_file.txt" "b/09E4T4oBgHgl3EQfzA3P/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/09E4T4oBgHgl3EQfzA3P/content/tmp_files/load_file.txt" @@ -0,0 +1,1346 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf,len=1345 +page_content='Observation of terahertz second harmonic generation from surface states in the topological insulator Bi2Se3 Jonathan Stensberg,1 Xingyue Han,1 Zhuoliang Ni,1 Xiong Yao,2, ∗ Xiaoyu Yuan,2 Debarghya Mallick,2 Akshat Gandhi,2 Seongshik Oh,2 and Liang Wu1, † 1Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='A 2Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' (Dated: January 16, 2023) We report the observation of second harmonic generation with high conversion efficiency ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='005% in the terahertz regime from thin films of the topological insulator Bi2Se3 that exhibit the linear photogalvanic effect, measured via time-domain terahertz spectroscopy and terahertz emission, re- spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The features of both phenomena are found to be consistent with the characteristics of and attributable to the surface of Bi2Se3, which breaks both inversion symmetry and two-fold rotation symmetry and therefore permits second-order processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Since both phenomena result from processes that reverse sign in oppositely-oriented domains of Bi2Se3, the observation of both phenomena is attributable to the presence of unequally populated twinned domains in the sample over millimeter length scales, confirmed by atomic force microscopy measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' These results represent the first observation of intrinsic terahertz second harmonic generation in an equilibrium system, unlocking the full suite of both even and odd harmonic orders in the terahertz regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Introduction Harmonic generation (HG) has been an invaluable non- linear optical technique since its first demonstration [1] and continues to power recent advances ranging from the imagining of microscopic magnetic domains [2, 3] to the development of tabletop sources of extreme ultraviolet and x-ray light for attosecond science [4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' However, since nth-order nonlinear optical processes scale with the nth power of the optical intensity, employing HG to study phenomena below ∼100 meV has been severely impeded by the historical terahertz (THz) gap [6], traditionally ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='1-30 THz (1 THz ≈ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='1 meV), where technical chal- lenges have impeded the development of intense light sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Recent progress in intense THz generation [7, 8], however, has enabled the first applications of HG to the THz regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Since its first demonstration [9], THz third harmonic generation (THG) has rapidly become a stan- dard tool for characterizing the Higgs mode [9–13] and other nonlinear optical processes [14–26] in a variety of superconductors [27–34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Yet more recently, odd-order THz-HG has been reported in doped Si [35, 36] and ma- terials hosting Dirac fermions, namely graphene [37–40], Cd3As2 [41–43], and the bismuth chalcogenide family of topological insulators [40, 44, 45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The latest stud- ies have explored controlling and optimizing THz-HG, demonstrating that the nonlinear process can be effec- tively tuned via gating [38] and metasurfacing [39, 40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Despite these exciting advances, THz-HG remains highly constrained, limited to odd-order low harmon- ics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Most strikingly, intrinsic even-order THz harmonics, which are only generated in systems that break inversion ∗ Current Affiliation: Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China † liangwu@sas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='upenn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='edu symmetry, have never been demonstrated in an equilib- rium material, having been observed only in supercon- ductors with a net propagating supercurrent [46, 47] or in carefully engineered devices [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The lack of THz second harmonic generation (SHG) in the studies of the bismuth chalcogenides [40, 44, 45] is of particular note, as SHG–and even-order HG in general–originating from the surface has been a well-established feature of the nonlin- ear optical response outside of the THz regime [49–55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Furthermore, as the bismuth chalcogenides are prototyp- ical topological insulators [56–59] with a centrosymmet- ric bulk and inversion symmetry-breaking surfaces, the second-order optical response of THz-SHG offers a path- way to measuring the properties of the topological sur- face state while intrinsically avoiding the properties of the bulk band, without resorting to doping [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Here, we report the observation of THz-SHG from Bi2Se3 samples exhibiting the linear photogalvanic effect (LPGE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' With LPGE determined by THz emission [60] and THz-SHG measured via intense time-domain THz spectroscopy (TDTS) [61], thin films of Bi2Se3 that display LPGE are found to produce THz-SHG that is highly efficient and independent of the sam- ple thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' As both LPGE and SHG result from second-order nonlinear processes, both effects originate from the three-fold symmetric surface of Bi2Se3, which breaks both inversion symmetry and two-fold rotation symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' We further show that the observation of both LPGE and THz-SHG is dependent upon the presence of unequally populated twinned domains in the sample, since twinned (oppositely-oriented) domains produce oppositely-signed second-order responses in such a three-fold symmetry system, which tend to cancel out (See the supplementary information (SI) for the derivation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' These results represent the first observation of intrinsic SHG in the THz regime for an equilibrium system, to our knowledge, and thereby open arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='05271v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='str-el] 12 Jan 2023 2 the investigation of material properties via THz-HG to the full suite of harmonic orders, both even and odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The dependence of both the LPGE and THz-SHG upon the presence of untwinned domains further motivates the future development of techniques to preferentially control the orientation of crystal growth on millimeter scales, particularly for materials that break various symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Results and Discussion Thin film samples of Bi2Se3 are grown via molecular beam epitaxy on c-axis Al2O3 substrates (10 mm x 10 mm x 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5 mm), following the two-step growth process [62, 63] to prevent disorder at the sample-substrate interface and achieve atomically sharp interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The samples are then capped in situ with 50 nm of Se to protect against damage and the effects of atmosphere [45, 49, 51, 53, 64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' As each van der Waals unit of Bi2Se3 is formed of a quintuple layer (QL) of Bi2Se3 (1 QL ≈ 1 nm), samples with thicknesses 16 QL, 32 QL, 64 QL, and 100 QL are grown to form a thickness series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The samples of Bi2Se3 are evaluated for their room temperature LPGE response by measuring the THz emis- sion [60] of the samples under normal incidence, near in- frared (NIR) pumping at the center wavelength of 1530 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' When a single domain of Bi2Se3 is pumped with NIR, the LPGE produces a current across the domain [65, 66], which couples out to free space as a THz pulse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' This emitted THz pulse is generated and detected by a THz emission spectrometer depicted schematically in Fig 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='a and described in previous works [67, 68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' In brief, the sample is pumped over a spot size of order 1 mm by lin- early polarized, broadband 1530 nm, 50 fs pulses with a repetition rate of 1 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' A quasi-single cycle THz pulse is emitted from the sample in transmission geometry;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' col- lected, collimated, and focused onto a ZnTe crystal by a pair of off-axis parabolic mirrors in 4f geometry;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' and measured via electro-optic sampling [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' By varying the optical path length of the NIR probe pulse via the delay stage, the electric field profile of the emitted THz pulse ET Hz is mapped out in the time domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' THz emission data is depicted in Fig 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='b,c for a typical 100 QL Bi2Se3 sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' As shown in 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='b, a pronounced quasi-single cycle THz pulse is emitted upon NIR pump- ing, the polarity of which changes sign throughout the duration of the pulse when the sample is rotated az- imuthally by 180 degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' By tracing out the peak value of ET Hz as the sample is rotated, as shown in Fig 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='c, the azimuthal angle dependence clearly follows Emax T Hz = E0 sin (3φ + φ0), where E0 is the peak electric field strength, φ is the azimuthal angle, and φ0 is an ar- bitrary angle difference between the crystalline axes and the lab frame for a given sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' See SI for derivation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' This sin (3φ) dependence of the emitted ET Hz is pre- cisely the azimuthal angle dependence expected for THz emission from a single domain of Bi2Se3 due to LPGE under normal incidence [49–52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' LPGE is only per- mitted in systems that break inversion symmetry [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' a b c FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Schematic of the THz emission spectrometer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The NIR and THz beam paths are depicted in magenta and green, respectively, and the THz beam path is contained in a dry air- purged box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Both sample (S) and polarizer (P) are mounted in rotating stages to enable characterization of the azimuthal angle dependence of the THz emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Labeled optical ele- ments include beam splitter (BS), pelical (Pel), ZnTe crystal (ZnTe), quarter wave plate (QWP), Wollaston prism (WP), photodiodes (PD), and delay stage (DS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Normalized elec- tric field profile of the emitted THz pulse from Se-capped 100 QL Bi2Se3 obtained by electro-optic sampling mapped in the time domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The peak normalized electric field as the sample azimuthal angle φ is rotated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' As bulk Bi2Se3 is centrosymmetric, only the surface of Bi2Se3 breaks inversion symmetry, and hence, only the surface contributes to the LPGE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Since the surface of Bi2Se3 is three-fold symmetric and breaks two-fold ro- tation symmetry, the normal-incidence LPGE from the surface must also be three-fold symmetric with respect to the azimuthal angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' This yields a sin (3φ) dependence of the LPGE current, which when coupled out to free space, OAP Pel BS S ZnTe P WP DS QWP PD1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0- THz Field (norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=') 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5- 180° 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5- 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0- 0 1 2 3 4 Time Delay (ps) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0 Peak THz Field (norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=') 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0- 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5- 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0- 0 50 100 150 200 250 300 350 Azimuthal Angle (degrees)3 c d a b FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Schematic of the intense TDTS system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The NIR and THz beam paths are depicted in magenta and green, respectively, and the THz beam path is contained in a dry air-purged box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Labeled optical elements include sample (S), LiNbO3 crystal (LiNbO3), THz filters (F1 and F2), diffraction grating (DG), beam splitter (BS), pelical (Pel), ZnTe crystal (ZnTe), quarter wave plate (QWP), Wollaston prism (WP), photodiodes (PD), and delay stage (DS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Harmonic generation spectra for Se-capped Bi2Se3 samples under a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5 THz fundamental pump with respect to a reference substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The change between spectra taken with 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0 THz-specific and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5 THz-specific filters are indicated by breaks in the spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Peak spectral weight at the 2nd and 3rd harmonic as a function of the peak 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5 THz pump field Epump, with fits to E2 pump and E3 pump respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Peak spectral weight at the 2nd and 3rd harmonics as function of sample thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' results in the Emax T Hz = E0 sin (3φ) dependence of the THz emission observed here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' However, since the spot size of the NIR pump (order 1 mm) vastly exceeds the domain size of Bi2Se3 (order 1 µm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' see Fig 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='c,d), the THz emis- sion method measures the net LPGE produced by a large ensemble of Bi2Se3 domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Since twinned domains in the sample produce oppositely-signed LPGE responses, as demonstrated in Fig 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='b, and hence cancel each other out, the observation of a clear LPGE signal from the sam- ple therefore indicates the presence of a dominant domain orientation over millimeter length scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' As SHG is limited by the same symmetry considera- tions as LPGE and expected to be generated from the surface of Bi2Se3 [49–52], the THz-HG of the samples is measured via intense TDTS [61] at room temperature as shown schematically in Fig 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Intense broadband, quasi-single cycle THz pulses are generated from LiNbO3 via the tilted pulse front method [70–72] by pumping with linearly polarized, broadband 800 nm, 35 fs pulses with a repetition rate of 1 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The generated intense THz pulses are collected, directed through the sample at a waist of order 1 mm, and focused onto a ZnTe crys- tal by a quartet of OAPs in 8f geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Prior to the sample, optical filters (F1) convert the broadband pulse into a narrow-band few cycle pulse centered at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5 THz (spectral width ∼ 20%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' After transmitting through the sample, the resulting THz pulse is passed through op- tical filters (F2) to suppress the spectral weight of the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5 THz fundamental pulse and pass the frequency range around the harmonic to be observed: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0 THz for SHG or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5 THz for THG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The remaining THz that impinges upon the ZnTe crystal is measured by standard electro- optic sampling [69], allowing the electric field profile to be mapped out in the time domain by varying the de- lay stage of the probe pulse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Finally, taking the Fourier transform of the THz pulse in the time domain yields the spectral weight of the pulse as a function of frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The HG spectra for the Bi2Se3 samples shown in Fig Substr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Spectral Weight (norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=') Fund.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' 16 QL 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='1 32 QL 64 QL 100 QL 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='001 11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='8 Frequency (THz) norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=', 亚 norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' 20 20 2nd Harmonic TO 3rd Harmonic Harmonic Peak (x10~ 15 Harmonic Peak (x10~ 16 2nd Harmonic 10 0 3rd Harmonic 12 5 8- 0 20 25 30 35 40 45 0 20 40 60 80 100 Pump Field (kV/cm) Sample Thickness (QL)LiNbO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' BS DG F1 OAP S F2 OAP Pel DS PD ZnTe Wp QWP4 a b d c FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' a,b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Comparison of THz-SHG and LPGE, respectively, for two bare 100 QL Bi2Se3 samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The azimuthal angle in (b) is offset for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' c,d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Atomic force microscopy images of bare 100 QL Bi2Se3 for Sample 1 and Sample 2, respectively, where oppositely-oriented domains on the surface are highlighted with blue and red boxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='b exhibit clear THz-SHG at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0 THz and THz-THG at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5 THz when pumping with the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5 THz funda- mental.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Three key features of the THz-THG response demonstrate strong agreement with the previous THz- HG studies [40, 44, 45] of bismuth chalcogenides: First, the THG conversion efficiency is ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='04% (accounting for the THG-specific filters), which closely matches the con- version efficiency in previous reports.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Second, the yield of the THz-THG scales perturbatively as E3 pump, as shown in Fig 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='c which is likewise in agreement with previous results and contrasting sharply with the saturation of harmonic yield observed in graphene [37–40] and Cd3As2 [41, 42] at similar THz pumping field strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Third, the THz-THG yield is nearly thickness-independent, as shown in Fig 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='d, which is consistent with the conclu- sion that the dominant contribution to the THz-THG is the response of the topological surface state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Together, these features of the THz-THG reaffirm the results of the previous studies and demonstrate that the intrinsic non- linear properties of the Bi2Se3 samples measured here are consistent with those of the previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Returning to Fig 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='b, however, a clear THz-SHG peak is observed at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0 THz, in addition to the THz-THG peak at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5 THz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' As shown in Fig 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='c, the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0 THz peak scales according to the E2 pump expectation for a pertur- bative second-order response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' And since only the surface of Bi2Se3 breaks inversion symmetry and two-fold rota- tion symmetry as required for a second order process, the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0 THz peak is found to be thickness independent, as dictated by the symmetry and shown in Fig 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' This clear THz-SHG response from Bi2Se3, which reaches a high conversion efficiency of ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='005% (accounting for the SHG-specific filters), is consistent with HG studies outside of the THz regime [49–55], but contrasts sharply with the previous THz studies [40, 44, 45] of bismuth chalcogenides, which failed to report THz-SHG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' We turn then to the question of why THz-SHG is observed here but not in previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Since both LPGE and SHG are second-order processes that require the breaking of inversion symmetry, which only occurs at the Bi2Se3 surface, both processes are governed by the same crystal properties of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Hence, both processes are expected to be observed in single crystals of Bi2Se3, but may be diminished by the presence of twinned domains when probing an ensemble of domains, as is the case for the relatively large spot sizes employed both here and in the previous THz-HG studies [40, 44, 45] of bismuth chalcogenides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Thus it may be possible that twinned domains suppressed the THz-SHG below the ob- servable level of the previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' This possibility is confirmed by comparing samples of Bi2Se3 that have been grown without the 50 nm Se cap- ping layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Fig 3 compares the results for two 100 QL bare Bi2Se3 samples taken from the same batch to en- sure similar growth quality and similar exposure to at- mosphere [45, 49, 51, 53, 64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The two samples show a clear difference in both THz-SHG and LPGE, shown in Fig 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='a,b, respectively, where Sample 1 shows a con- sistently smaller second-order response than Sample 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Since both samples are not capped, the orientation of surface domains can be determined by atomic force mi- croscopy (AFM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' As shown in Fig 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='c,d, respectively, AFM clearly reveals twinned domains on the surface of both Sample 1 and Sample 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' A careful counting of these domains shows that the ratio of oppositely-oriented do- mains is ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5 : 1 in Sample 1 and ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='8 : 1 in Sample 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Since Sample 1 has a lesser degree of untwinned domains than Sample 2, it should produce a lesser degree of THz- SHG and LPGE, precisely as observed in these measure- ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Since the ordinary growth of Bi2Se3 tends to pro- duce samples with twinned domains that suppresses both LPGE and THz-SHG, as shown here, a sufficiently high degree of twinned domains could suppress both effects below the noise level of current measurement techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' 0 Spectral Weight (x10* 8 Sample 1 Sample 2 6 2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='2 Frequency (THz) Peak THz Field (norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=') Sample 1 Sample 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='0 0 100 200 300 Azimuthal Angle (degrees)6 8- im 5 nm 3 4 0 0 1 2 3 4 5 6 7 8 9 10 μm40 9 3 8 30 20 L 15 10 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='92 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='01 2 4 5 6 8 6 10 μm5 This problem of twinned domains therefore presents one potential reason why that the previous studies [40, 44, 45] of bismuth chalcogenides failed to report THz-SHG, and it highlights the importance of improving control over crystal growth to enable more reliable experimental re- sults, particularly for materials that break various sym- metries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' To summarize, we have observed THz-SHG from Bi2Se3 thin films that exhibit LPGE as measured via intense TDTS and THz emission, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Moreover, the THz-SHG may be attributed to the topological surface state of the Bi2Se3 and features a highly efficient conversion rate of ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='005% that is independent of the film thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' These results extend beyond previous studies [40, 44, 45] of similar topological insulator bismuth chalcogenides, which reported only odd-order harmonics, and furthermore represent the first demonstration of intrinsic SHG–or indeed any even-order HG–in the THz regime for an equilibrium system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' This advance enables and motivates further development of HG techniques for the characterization of material properties and the development of useful devices in the THz regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' In particular, THz-HG employing circularly and elliptically polarized light remains in its infancy [43], despite the discovery of highly nonlinear dependencies [55, 73–76] in high har- monic generation [77, 78] studies employing mid-infrared fundamentals, and despite the recent demonstration of elliptically polarized harmonics as an effective probe of topological properties [55, 79, 80].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' This highlights the need to develop higher performance and more widely available THz optical elements, especially waveplates [81, 82], which have been historically limited due to the broadband nature of THz techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Furthermore, the connection between untwinned domains and THz-SHG in Bi2Se3, a member of the broader bismuth chalcogenide family that serves as standard topological insulators in myriad studies, highlights the need to develop growth methods that reliably produce untwinned domains over millimeter scales, especially if the preferential growth orientation can be controlled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Altogether, these results vastly expand the possible range of future studies by unlocking even-order HG in the THz regime, open a new pathway to the low-energy study of topological surface states, and motivate further efforts to develop efficient THz optical elements and material growth techniques that yield untwinned domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Acknowledgement We thank J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Lu for helpful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' This project was sponsored by the Army Research Office and was accomplished under the grants no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' W911NF-20-2-0166 and W911NF-19-1-0342.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' was also supported by the NSF EAGER grant via the CMMT programme (DMR- 2132591) and the Gordon and Betty Moore Foundation’s EPiQS Initiative under the grant GBMF9212 to L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='. X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' is supported by the NSF EPM program under grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' DMR-2213891.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' acknowledges support from the Vagelos Institute of Energy Science and Technology grad- uate fellowship and the Dissertation Completion Fellow- ship at the University of Pennsylvania.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' The work at Rutgers by X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Yao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' Yuan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=', A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09E4T4oBgHgl3EQfzA3P/content/2301.05271v1.pdf'} +page_content=' G.' metadata={'source': 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