alx-ai/arxiv_papers · Datasets at Hugging Face

text stringlengths 0 44.4k
[26] A. D. Linde, Phys. Rev. D 49, 748 (1994) [arXiv:astro-
ph/9307002].
[27] Z. Komargodski and N. Seiberg, JHEP 0909 , 066 (2009)[arXiv:0907.2441 [hep-th]].
[28] D. V. Volkov and V. P. Akulov, Phys. Lett. B 46, 109 (1973).
[29] S. Ferrara and B. Zumino, Nucl. Phys. B 87, 207 (1975).
[30] E. Cremmer, B. Julia, J. Scherk, P. van Nieuwenhuizen, S. Fer-
rara and L. Girardello, Phys. Lett. B 79, 231 (1978), E. Crem-
mer, B. Julia, J. Scherk, S. Ferrara, L. Girardello and P. van
Nieuwenhuizen, Nucl. Phys. B 147, 105 (1979).
8
arXiv:1001.0011v2 [cond-mat.mes-hall] 16 Apr 2010Guided plasmons in graphene p-njunctions
E. G. Mishchenko,1A. V. Shytov∗,1and P. G. Silvestrov2
1Department of Physics and Astronomy, University of Utah, Sa lt Lake City, Utah 84112, USA
2Theoretische Physik III, Ruhr-Universit¨ at Bochum, 44780 Bochum, Germany
Spatial separation of electrons and holes in graphene gives rise to existence of plasmon waves
conﬁned to the boundary region. Theory of such guided plasmo n modes within hydrodynamics of
electron-hole liquid is developed. For plasmon wavelength s smaller than the size of charged domains
plasmon dispersion is found to be ω∝q1/4. Frequency, velocity and direction of propagation of
guided plasmon modes can be easily controlled by external el ectric ﬁeld. In the presence of magnetic
ﬁeld spectrum of additional gapless magnetoplasmon excita tions is obtained. Our ﬁndings indicate
that graphene is a promising material for nanoplasmonics.
PACS numbers: 73.23.-b, 72.30.+q
Introduction . Breakthrough progress in synthesis and
characterization has made graphene [2] a promising ob-
ject for nanoelectronics. Operation of graphene-based
transistors [3] and other components would rely on the
propertiesofits single-particle excitations–electronsand
holes. However, one can also envisage a completely dif-
ferent set of applications which employ collective excita-
tions, such as plasmons. Currently, plasmon excitations
in metallic structures are a subject of nanoplasmonics, a
new ﬁeld which has emerged at the conﬂuence of optics
and condensed matter physics with one of the aims be-
ing the developing of plasmon-enhanced high resolution
near-ﬁeld imaging methods [4, 5]. Another objective is
possible utilization of plasmons in integrated optical cir-
cuits. However, perspectives of graphene for nanoplas-
monics are largely unexplored since plasmon modes of
graphene ﬂakes have not been addressed so far. As our
results indicate a great amount of control over graphene
plasmon properties makes it a very promising material
for applications.
Fundamentally, the spectrum of collective chargeoscil-
lations reﬂects the long-rangenature of Coulomb interac-
tion. In conventional two dimensional systems, such as
those created in semiconducting heterostructures, plas-
mons are gapless, ω2(q) = 2πe2nq/m∗, withnandm∗
being electron density and eﬀective mass, respectively
[6]. Such oscillations can be treated hydrodynamically.
In clean graphene at zero temperature the plasmon fre-
quency,ω2∝ \|EF\|, vanishes with decreasing the doping
levelEF. It has been argued [7] that the interaction be-
tweenelectronsandholesintheﬁnalstatecanmodifythe
response functions of Dirac fermions and open up a pos-
sibility for the propagation of charge oscillations at low
frequencies ω < qv, wherevis electron velocity. Still, hy-
drodynamic( ω > qv)analogofconventionalplasmonsre-
mains absent unless either temperature is non-zero [8] or
graphene is driven away from the charge neutrality point
by doping or gating [9]. Expectedly, in both cases plas-
mon spectrum has the conventional form, ω(q)∝q1/2.
In the present paper we investigate spectra of hydro-
dynamic plasmons in spatially inhomogeneous grapheneﬂakes. Realistic graphene samples are typically subject
to disorder potential and mechanical strain [10] that lead
totheformationofchargedelectronandholepuddles[11]
with boundaries between nandpregions being the lines
ofzerochemicalpotential. Moreover,controlled p-njunc-
tions can be made with the help of metallic gates [12].
Alsop-njunctions can be created by applying electric
ﬁeld within the plane of a graphene ﬂake, see Fig. 1a.
The ﬁeld separates electrons and holes spatially in a way
that allows control of both the amount of induced charge
(and thus plasmon frequency) and spatial orientation of
the junction (the direction of plasmon propagation).
b)2d 2d
Ea)
0n n
p p
FIG.1: Twotypesofgraphene p-njunctions: a)ﬁeld-induced,
b) gate-induced. Dot-dashed line indicates boundary betwe en
electron and hole regions and, correspondingly, the direct ion
of plasmon propagation. In case of ﬁeld-induced junction it
is controlled by the direction of external electric ﬁeld E0.
Below, we demonstrate that such p-njunctions can
guide plasmons. We show the existence of charge oscil-
lations which are localized at the junction and have the
amplitude decaying with the distance to the junction.
For wavelengths shorter than the width of the charged
domains, we ﬁnd the plasmon spectrum of the form,
ω2
n(q) =αne2v
¯h/radicalbigg
q\|ρ′
0\|
e, (1)
whereρ′
0is the gradient of equilibrium charge density
at the junction, vis electron velocity, and n= 0,1,2,...2
enumerates the solutions. The lowest mode has α0=
4√

[26] A. D. Linde, Phys. Rev. D 49, 748 (1994) [arXiv:astro-

ph/9307002].

[27] Z. Komargodski and N. Seiberg, JHEP 0909 , 066 (2009)[arXiv:0907.2441 [hep-th]].

[28] D. V. Volkov and V. P. Akulov, Phys. Lett. B 46, 109 (1973).

[29] S. Ferrara and B. Zumino, Nucl. Phys. B 87, 207 (1975).

[30] E. Cremmer, B. Julia, J. Scherk, P. van Nieuwenhuizen, S. Fer-

rara and L. Girardello, Phys. Lett. B 79, 231 (1978), E. Crem-

mer, B. Julia, J. Scherk, S. Ferrara, L. Girardello and P. van

Nieuwenhuizen, Nucl. Phys. B 147, 105 (1979).

8

arXiv:1001.0011v2 [cond-mat.mes-hall] 16 Apr 2010Guided plasmons in graphene p-njunctions

E. G. Mishchenko,1A. V. Shytov∗,1and P. G. Silvestrov2

1Department of Physics and Astronomy, University of Utah, Sa lt Lake City, Utah 84112, USA

2Theoretische Physik III, Ruhr-Universit¨ at Bochum, 44780 Bochum, Germany

Spatial separation of electrons and holes in graphene gives rise to existence of plasmon waves

conﬁned to the boundary region. Theory of such guided plasmo n modes within hydrodynamics of

electron-hole liquid is developed. For plasmon wavelength s smaller than the size of charged domains

plasmon dispersion is found to be ω∝q1/4. Frequency, velocity and direction of propagation of

guided plasmon modes can be easily controlled by external el ectric ﬁeld. In the presence of magnetic

ﬁeld spectrum of additional gapless magnetoplasmon excita tions is obtained. Our ﬁndings indicate

that graphene is a promising material for nanoplasmonics.

PACS numbers: 73.23.-b, 72.30.+q

Introduction . Breakthrough progress in synthesis and

characterization has made graphene [2] a promising ob-

ject for nanoelectronics. Operation of graphene-based

transistors [3] and other components would rely on the

propertiesofits single-particle excitations–electronsand

holes. However, one can also envisage a completely dif-

ferent set of applications which employ collective excita-

tions, such as plasmons. Currently, plasmon excitations

in metallic structures are a subject of nanoplasmonics, a

new ﬁeld which has emerged at the conﬂuence of optics

and condensed matter physics with one of the aims be-

ing the developing of plasmon-enhanced high resolution

near-ﬁeld imaging methods [4, 5]. Another objective is

possible utilization of plasmons in integrated optical cir-

cuits. However, perspectives of graphene for nanoplas-

monics are largely unexplored since plasmon modes of

graphene ﬂakes have not been addressed so far. As our

results indicate a great amount of control over graphene

plasmon properties makes it a very promising material

for applications.

Fundamentally, the spectrum of collective chargeoscil-

lations reﬂects the long-rangenature of Coulomb interac-

tion. In conventional two dimensional systems, such as

those created in semiconducting heterostructures, plas-

mons are gapless, ω2(q) = 2πe2nq/m∗, withnandm∗

being electron density and eﬀective mass, respectively

[6]. Such oscillations can be treated hydrodynamically.

In clean graphene at zero temperature the plasmon fre-

quency,ω2∝ |EF|, vanishes with decreasing the doping

levelEF. It has been argued [7] that the interaction be-

tweenelectronsandholesintheﬁnalstatecanmodifythe

response functions of Dirac fermions and open up a pos-

sibility for the propagation of charge oscillations at low

frequencies ω < qv, wherevis electron velocity. Still, hy-

drodynamic( ω > qv)analogofconventionalplasmonsre-

mains absent unless either temperature is non-zero [8] or

graphene is driven away from the charge neutrality point

by doping or gating [9]. Expectedly, in both cases plas-

mon spectrum has the conventional form, ω(q)∝q1/2.

In the present paper we investigate spectra of hydro-

dynamic plasmons in spatially inhomogeneous grapheneﬂakes. Realistic graphene samples are typically subject

to disorder potential and mechanical strain [10] that lead

totheformationofchargedelectronandholepuddles[11]

with boundaries between nandpregions being the lines

ofzerochemicalpotential. Moreover,controlled p-njunc-

tions can be made with the help of metallic gates [12].

Alsop-njunctions can be created by applying electric

ﬁeld within the plane of a graphene ﬂake, see Fig. 1a.

The ﬁeld separates electrons and holes spatially in a way

that allows control of both the amount of induced charge

(and thus plasmon frequency) and spatial orientation of

the junction (the direction of plasmon propagation).

b)2d 2d

Ea)

0n n

p p

FIG.1: Twotypesofgraphene p-njunctions: a)ﬁeld-induced,

b) gate-induced. Dot-dashed line indicates boundary betwe en

electron and hole regions and, correspondingly, the direct ion

of plasmon propagation. In case of ﬁeld-induced junction it

is controlled by the direction of external electric ﬁeld E0.

Below, we demonstrate that such p-njunctions can

guide plasmons. We show the existence of charge oscil-

lations which are localized at the junction and have the

amplitude decaying with the distance to the junction.

For wavelengths shorter than the width of the charged

domains, we ﬁnd the plasmon spectrum of the form,

ω2

n(q) =αne2v

¯h/radicalbigg

q|ρ′

0|

e, (1)

whereρ′

0is the gradient of equilibrium charge density

at the junction, vis electron velocity, and n= 0,1,2,...2

enumerates the solutions. The lowest mode has α0=

4√