Here, we report on a transparent method to characterize individual layers in a double-layer electron system, which forms in a wide quantum well, and to determine their electron densities. The technique relies on the simultaneous measurement of the capacitances between the electron system and gates located on either side of the well. Modifications to the electron wave function due to the population of the second subband and the appearance of an additional electron layer can be detected. The magnetic field dependence of these capacitances is dominated by quantum corrections caused by the occupation of Landau levels in the nearest electron layer. The technique should be equally applicable to other implementations of a double layer electron system.
References
1.
See experimental chapter by J. P. Eisenstein and theoretical chapter by
S. M.
Girvin
and A. H.
MacDonald
, in Perspectives on Quantum Hall Effects
, edited by S.
Das Sarma
and A.
Pinczuk
(Wiley
, New York
, 1997
).2.
J. P.
Eisenstein
, “Exciton condensation in bilayer quantum Hall systems
,” Annu. Rev. Condens. Matter Phys.
5
, 159
(2014
).3.
H.
Min
, R.
Bistritzer
, J.-J.
Su
, and A. H.
MacDonald
, “Room-temperature superfluidity in graphene bilayers
,” Phys. Rev. B
78
, 121401
(2008
).4.
A.
Perali
, D.
Neilson
, and A. R.
Hamilton
, “High-temperature superfluidity in double-bilayer graphene
,” Phys. Rev. Lett.
110
, 146803
(2013
).5.
K.
Lee
, B.
Fallahazad
, J.
Xue
, D. C.
Dillen
, K.
Kim
, T.
Taniguchi
, K.
Watanabe
, and E.
Tutuc
, “Chemical potential and quantum Hall ferromagnetism in bilayer graphene
,” Science
345
, 58
(2014
).6.
X.
Liu
, K.
Watanabe
, T.
Taniguchi
, B. I.
Halperin
, and P.
Kim
, “Quantum Hall drag of exciton condensate in graphene
,” Nat. Phys.
13
, 746
(2017
).7.
G. S.
Boebinger
, H. W.
Jiang
, L. N.
Pfeiffer
, and K. W.
West
, “Magnetic-field-driven destruction of quantum Hall states in a double quantum well
,” Phys. Rev. Lett.
64
, 1793
(1990
).8.
Y. W.
Suen
, J.
Jo
, M. B.
Santos
, L. W.
Engel
, S. W.
Hwang
, and M.
Shayegan
, “Missing integral quantum Hall effect in a wide single quantum well
,” Phys. Rev. B
44
, 5947
(1991
).9.
J. P.
Eisenstein
, L. N.
Pfeiffer
, and K. W.
West
, “Independently contacted two-dimensional electron systems in double quantum wells
,” Appl. Phys. Lett.
57
, 2324
(1990
).10.
U. S.
de Cumis
, J.
Waldie
, A. F.
Croxall
, D.
Taneja
, J.
Llandro
, I.
Farrer
, H. E.
Beere
, and D. A.
Ritchie
, “A complete laboratory for transport studies of electron-hole interactions in GaAs/AlGaAs ambipolar bilayers
,” Appl. Phys. Lett.
110
, 072105
(2017
).11.
I. B.
Spielman
, J. P.
Eisenstein
, L. N.
Pfeiffer
, and K. W.
West
, “Resonantly enhanced tunneling in a double layer quantum Hall ferromagnet
,” Phys. Rev. Lett.
84
, 5808
(2000
).12.
M.
Kellogg
, I. B.
Spielman
, J. P.
Eisenstein
, L. N.
Pfeiffer
, and K. W.
West
, “Observation of quantized Hall drag in a strongly correlated bilayer electron system
,” Phys. Rev. Lett.
88
, 126804
(2002
).13.
D. R.
Leadley
, R.
Fletcher
, R. J.
Nicholas
, F.
Tao
, C. T.
Foxon
, and J. J.
Harris
, “Intersubband resonant scattering in heterojunctions
,” Phys. Rev. B
46
, 12439
(1992
).14.
N. C.
Mamani
, G. M.
Gusev
, T. E.
Lamas
, and A. K.
Bakarov
, “Resonance oscillations of magnetoresistance in double quantum wells
,” Phys. Rev. B
77
, 205327
(2008
).15.
16.
P. T.
Coleridge
, “Inter-subband scattering in a 2D electron gas
,” Semicond. Sci. Technol.
5
, 961
(1990
).17.
M. E.
Raikh
and T. V.
Shahbazyan
, “Magnetointersubband oscillations of conductivity in a two-dimensional electronic system
,” Phys. Rev. B
49
, 5531
(1994
).18.
A. G.
Davies
, C. H. W.
Barnes
, K. R.
Zolleis
, J. T.
Nicholls
, M. Y.
Simmons
, and D. A.
Ritchie
, “Hybridization of single- and double-layer behavior in a double-quantum-well structure
,” Phys. Rev. B
54
, R17331
(1996
).19.
S. I.
Dorozhkin
, “Quantum Hall effect in a system with an electron reservoir
,” JETP Lett.
103
, 513
(2016
)20.
See http://link.aps.org/supplemental/10.1103/PhysRevB.89.081306 for the Supplementary Material.
21.
F.
Nichele
, A. N.
Pal
, R.
Winkler
, C.
Gerl
, W.
Wegscheider
, T.
Ihn
, and K.
Ensslin
, “Spin-orbit splitting and effective masses in p-type GaAs two-dimensional hole gases
,” Phys. Rev. B
89
, 081306(R)
(2014
).22.
T. P.
Smith
, B. B.
Goldberg
, P. J.
Stiles
, and M.
Heiblum
, “Direct measurement of the density of states of a two-dimensional electron gas
,” Phys. Rev. B
32
, 2696(R)
(1985
).23.
S. V.
Kravchenko
, V. M.
Pudalov
, and S. G.
Semenchinsky
, “Negative density of states of 2D electrons in a strong magnetic field
,” Phys. Lett. A
141
, 71
(1989
).24.
J. P.
Eisenstein
, L. N.
Pfeiffer
, and K. W.
West
, “Negative compressibility of interacting two-dimensional electron and quasiparticle gases
,” Phys. Rev. Lett.
68
, 674
(1992
).25.
S. V.
Kravchenko
, M.
Caulfield
, J.
Singleton
, H.
Nielsen
, and V. M.
Pudalov
, “Electron-electron interactions in the two-dimensional electron gas in silicon
,” Phys. Rev. B
47
, 12961
(1993
).26.
S. I.
Dorozhkin
, J. H.
Smet
, K.
von Klitzing
, V.
Umansky
, R. J.
Haug
, and K.
Ploog
, “Comparison between the compressibilities of the zero field and composite-fermion metallic states of the two-dimensional electron system
,” Phys. Rev. B
63
, 121301
(2001
).27.
S. I.
Dorozhkin
, G. V.
Kravchenko
, R. J.
Haug
, K.
von Klitzing
, and K.
Ploog
, “Capacitance spectroscopy of the fractional quantum Hall effect: Temperature dependence of the energy gap
,” JETP Lett.
58
, 834
(1993
)S. I.
Dorozhkin
, G. V.
Kravchenko
, R. J.
Haug
, K.
von Klitzing
, and K.
Ploog
, [Pis'ma Zh. Eksp. Teor. Fiz.
58
, 893
(1993
)].28.
J. P.
Eisenstein
, L. N.
Pfeiffer
, and K. W.
West
, “Compressibility of the two-dimensional electron gas: Measurements of the zero-field exchange energy and fractional quantum Hall gap
,” Phys. Rev. B
50
, 1760
(1994
).29.
S. I.
Dorozhkin
, R. J.
Haug
, K.
von Klitzing
, and K.
Ploog
, “Experimental determination of the quasiparticle charge and the energy gap in the fractional quantum Hall effect
,” Phys. Rev. B
51
, 14729
(1995
).30.
V. S.
Khrapai
, A. A.
Shashkin
, M. G.
Trokina
, V. T.
Dolgopolov
, V.
Pellegrini
, F.
Beltram
, G.
Biasiol
, and L.
Sorba
, “Direct measurements of fractional quantum Hall effect gaps
,” Phys. Rev. Lett.
99
, 086802
(2007
).31.
V. S.
Khrapai
, A. A.
Shashkin
, and V. T.
Dolgopolov
, “Direct measurements of the spin and the cyclotron gaps in a 2D electron system in silicon
,” Phys. Rev. Lett.
91
, 126404
(2003
).32.
K.
Ensslin
, D.
Heitmann
, R. R.
Gerhardts
, and K.
Ploog
, “Population process of the upper subband in quantum wells
,” Phys. Rev. B
39
, 12993
(1989
).33.
V. T.
Dolgopolov
, G. E.
Tsydynzhapov
, A. A.
Shashkin
, E. V.
Deviatov
, F.
Hastreiter
, M.
Hartung
, A.
Wixforth
, K. L.
Campman
, and A. C.
Gossard
, “Magnetic-field-induced hybridization of electron subbands in a coupled double quantum well
,” Pisma Zh. Eksp. Teor. Fiz.
67
, 563
(1998
)V. T.
Dolgopolov
, G. E.
Tsydynzhapov
, A. A.
Shashkin
, E. V.
Deviatov
, F.
Hastreiter
, M.
Hartung
, A.
Wixforth
, K. L.
Campman
, and A. C.
Gossard
, [JETP Lett.
67
, 595
(1998
).34.
V. T.
Dolgopolov
, A. A.
Shashkin
, E. V.
Deviatov
, F.
Hastreiter
, M.
Hartung
, A.
Wixforth
, K. L.
Campman
, and A. C.
Gossard
, “Electron subbands in a double quantum well in a quantizing magnetic field
,” Phys. Rev. B
59
, 13235
(1999
).35.
S. I.
Dorozhkin
, A. A.
Shashkin
, N. B.
Zhitenev
, and V. T.
Dolgopolov
, ““Skin effect” and observation of nonuniform states of a 2D electron gas in a metal-insulator-semiconductor structure
,” JETP Lett.
44
, 241
(1986
)S. I.
Dorozhkin
, A. A.
Shashkin
, N. B.
Zhitenev
, and V. T.
Dolgopolov
, [Pis'ma Zh. Eksp. Teor. Fiz.
44
, 189
(1986
).36.
S.
Luryi
, “Quantum capacitance devices
,” Appl. Phys. Lett.
52
, 501
(1988
).37.
We note that this estimate assumes infinite electron compressibility in the layers, which affects its accuracy.
38.
I. S.
Millard
, N. K.
Patel
, M. Y.
Simmons
, E. H.
Linfield
, D. A.
Ritchie
, G. A. C.
Jones
, and M.
Pepper
, “Compressibility studies of double electron and double hole gas systems
,” Appl. Phys. Lett.
68
, 3323
(1996
).39.
D.
Zhang
, S.
Schmult
, V.
Venkatachalam
, W.
Dietsche
, A.
Yacoby
, K.
von Klitzing
, and J.
Smet
, “Local compressibility measurement of the quantum Hall state in a bilayer electron system
,” Phys. Rev. B
87
, 205304
(2013
).© 2018 Author(s).
2018
Author(s)
You do not currently have access to this content.
