We report on sub-terahertz photoconductivity under the magnetic field of a two dimensional topological insulator based on HgTe quantum wells. We perform a detailed visualization of Landau levels by means of photoconductivity measured at different gate voltages. This technique allows one to determine a critical magnetic field, corresponding to topological phase transition from inverted to normal band structure, even in almost gapless samples. The comparison with realistic calculations of Landau levels reveals a smaller role of bulk inversion asymmetry in HgTe quantum wells than it was assumed previously.
References
1.
W.
Knap
, S.
Nadar
, H.
Videlier
, S.
Boubanga-Tombet
, D.
Coquillat
, N.
Dyakonova
, F.
Teppe
, K.
Karpierz
, J.
Lusakowski
, M.
Sakowicz
, I.
Kasalynas
, D.
Seliuta
, G.
Valusis
, T.
Otsuji
, Y.
Meziani
, A.
El Fatimy
, S.
Vandenbrouk
, K.
Madjour
, D.
Theron
, and C.
Gaquiere
, “Field effect transistors for terahertz detection and emission
,” J. Infrared, Millimeter, Terahertz Waves
32
, 618
(2011
).2.
D. J.
Thouless
, M.
Kohmoto
, M. P.
Nightingale
, and M.
den Nijs
, “Quantized Hall conductance in a two-dimensional periodic potential
,” Phys. Rev. Lett.
49
, 405
–408
(1982
).3.
B. A.
Bernevig
, T. L.
Hughes
, and S.-C.
Zhang
, “Quantum spin Hall effect and topological phase transition in HgTe quantum wells
,” Science
314
, 1757
–1761
(2006
).4.
M.
König
, S.
Wiedmann
, C.
Brüne
, A.
Roth
, H.
Buhmann
, L. W.
Molenkamp
, X.-L.
Qi
, and S.-C.
Zhang
, “Quantum spin Hall insulator state in HgTe quantum wells
,” Science
318
, 766
–770
(2007
).5.
B.
Buttner
, C. X.
Liu
, G.
Tkachov
, E. G.
Novik
, C.
Brune
, H.
Buhmann
, E. M.
Hankiewicz
, P.
Recher
, B.
Trauzettel
, S. C.
Zhang
, and L. W.
Molenkamp
, “Single valley Dirac fermions in zero-gap HgTe quantum wells
,” Nat. Phys.
7
, 418
–422
(2011
).6.
G. M.
Gusev
, A. D.
Levin
, Z. D.
Kvon
, N. N.
Mikhailov
, and S. A.
Dvoretsky
, “Quantum Hall effect in n-p-n and n-2D topological insulator-n junctions
,” Phys. Rev. Lett.
110
, 076805
(2013
).7.
G. M.
Gusev
, E. B.
Olshanetsky
, Z. D.
Kvon
, N. N.
Mikhailov
, and S. A.
Dvoretsky
, “Linear magnetoresistance in HgTe quantum wells
,” Phys. Rev. B
87
, 081311
(2013
).8.
M.
Orlita
, K.
Masztalerz
, C.
Faugeras
, M.
Potemski
, E. G.
Novik
, C.
Brüne
, H.
Buhmann
, and L. W.
Molenkamp
, “Fine structure of zero-mode landau levels in HgTe/HgxCd1−xTe quantum wells
,” Phys. Rev. B
83
, 115307
(2011
).9.
M.
Zholudev
, F.
Teppe
, M.
Orlita
, C.
Consejo
, J.
Torres
, N.
Dyakonova
, M.
Czapkiewicz
, J.
Wróbel
, G.
Grabecki
, N.
Mikhailov
, S.
Dvoretskii
, A.
Ikonnikov
, K.
Spirin
, V.
Aleshkin
, V.
Gavrilenko
, and W.
Knap
, “Magnetospectroscopy of two-dimensional HgTe-based topological insulators around the critical thickness
,” Phys. Rev. B
86
, 205420
(2012
).10.
A. M.
Kadykov
, F.
Teppe
, C.
Consejo
, L.
Viti
, M. S.
Vitiello
, S. S.
Krishtopenko
, S.
Ruffenach
, S. V.
Morozov
, M.
Marcinkiewicz
, W.
Desrat
, N.
Dyakonova
, W.
Knap
, V. I.
Gavrilenko
, N. N.
Mikhailov
, and S. A.
Dvoretsky
, “Terahertz detection of magnetic field-driven topological phase transition in HgTe-based transistors
,” Appl. Phys. Lett.
107
, 152101
(2015
).11.
M. S.
Zholudev
, F.
Teppe
, S. V.
Morozov
, M.
Orlita
, C.
Consejo
, S.
Ruffenach
, W.
Knap
, V. I.
Gavrilenko
, S. A.
Dvoretskii
, and N. N.
Mikhailov
, “Anticrossing of landau levels in HgTe/CdHgTe (013) quantum wells with an inverted band structure
,” JETP Lett.
100
, 790
–794
(2015
).12.
E. Y.
Ma
, M. R.
Calvo
, J.
Wang
, B.
Lian
, M.
Muhlbauer
, C.
Brune
, Y.-T.
Cui
, K.
Lai
, W.
Kundhikanjana
, Y.
Yang
, M.
Baenninger
, M.
Konig
, C.
Ames
, H.
Buhmann
, P.
Leubner
, L. W.
Molenkamp
, S.-C.
Zhang
, D.
Goldhaber-Gordon
, M. A.
Kelly
, and Z.-X.
Shen
, “Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry
,” Nat. Commun.
6
, 7252
(2015
).13.
D. A.
Kozlov
, D.
Bauer
, J.
Ziegler
, R.
Fisher
, M. L.
Savchenko
, Z. D.
Kvon
, N. N.
Mikhailov
, S. A.
Dvoretsky
, and D.
Weiss
, “Probing quantum capacitance in a 3D topological insulator
,” Phys. Rev. Lett.
116
, 166802
(2016
).14.
L.
Vicarelli
, M. S.
Vitiello
, D.
Coquillat
, A.
Lombardo
, A. C.
Ferrari
, W.
Knap
, M.
Polini
, V.
Pellegrini
, and A.
Tredicucci
, “Graphene field-effect transistors as room-temperature terahertz detectors
,” Nat. Mater.
11
, 865
–871
(2012
).15.
W.
Knap
, M.
Dyakonov
, D.
Coquillat
, F.
Teppe
, N.
Dyakonova
, J.
Łusakowski
, K.
Karpierz
, M.
Sakowicz
, G.
Valusis
, D.
Seliuta
, I.
Kasalynas
, A.
El Fatimy
, Y. M.
Meziani
, and T.
Otsuji
, “Field effect transistors for terahertz detection: Physics and first imaging applications
,” J. Infrared, Millimeter, Terahertz Waves
30
, 1319
(2009
).16.
M.
Dyakonov
and M.
Shur
, “Shallow water analogy for a ballistic field effect transistor: New mechanism of plasma wave generation by dc current
,” Phys. Rev. Lett.
71
, 2465
–2468
(1993
).17.
M.
Sakowicz
, M. B.
Lifshits
, O. A.
Klimenko
, F.
Schuster
, D.
Coquillat
, F.
Teppe
, and W.
Knap
, “Terahertz responsivity of field effect transistors versus their static channel conductivity and loading effects
,” J. Appl. Phys.
110
, 054512
(2011
).18.
D. A.
Kozlov
, Z. D.
Kvon
, N. N.
Mikhailov
, and S. A.
Dvoretsky
, “Weak localization of Dirac fermions in HgTe quantum wells
,” JETP Lett.
96
, 730
–734
(2013
).19.
S.
Dvoretsky
, N.
Mikhailov
, Y.
Sidorov
, V.
Shvets
, S.
Danilov
, B.
Wittman
, and S.
Ganichev
, “Growth of HgTe quantum wells for IR to THz detectors
,” J. Electron. Mater.
39
, 918
–923
(2010
).20.
L.
Liao
, J.
Bai
, R.
Cheng
, Y.-C.
Lin
, S.
Jiang
, Y.
Qu
, Y.
Huang
, and X.
Duan
, “Sub-100 nm channel length graphene transistors
,” Nano Lett.
10
, 3952
–3956
(2010
).21.
A. K.
Geim
and K. S.
Novoselov
, “The rise of graphene
,” Nat. Mater.
6
, 183
–191
(2007
).22.
E. G.
Novik
, A.
Pfeuffer-Jeschke
, T.
Jungwirth
, V.
Latussek
, C. R.
Becker
, G.
Landwehr
, H.
Buhmann
, and L. W.
Molenkamp
, “Band structure of semimagnetic Hg1−yMnyTe quantum wells
,” Phys. Rev. B
72
, 035321
(2005
).23.
S.
Wiedmann
, A.
Jost
, C.
Thienel
, C.
Brüne
, P.
Leubner
, H.
Buhmann
, L. W.
Molenkamp
, J. C.
Maan
, and U.
Zeitler
, “Temperature-driven transition from a semiconductor to a topological insulator
,” Phys. Rev. B
91
, 205311
(2015
).24.
Mercury Cadmium Telluride—Growth, Properties and Applications
, edited by P.
Capper
and J.
Garland
(Wiley
, 2011
).25.
M.
König
, H.
Buhmann
, L. W.
Molenkamp
, T.
Hughes
, C.-X.
Liu
, X.-L.
Qi
, and S.-C.
Zhang
, “The quantum spin Hall effect: Theory and experiment
,” J. Phys. Soc. Jpn.
77
, 031007
(2008
).26.
M. V.
Durnev
and S. A.
Tarasenko
, “Magnetic field effects on edge and bulk states in topological insulators based on HgTe/CdHgTe quantum wells with strong natural interface inversion asymmetry
,” Phys. Rev. B
93
, 075434
(2016
).27.
W.-K.
Tse
and A. H.
MacDonald
, “Interaction effects in the optical conductivity of bilayer graphene: Drude-interband coupling and screening
,” Phys. Rev. B
80
, 195418
(2009
).28.
K.
Shizuya
, “Many-body corrections to cyclotron resonance in monolayer and bilayer graphene
,” Phys. Rev. B
81
, 075407
(2010
).29.
V. E.
Bisti
and N. N.
Kirova
, “Coulomb interaction and electron-hole asymmetry in cyclotron resonance of bilayer graphene in a high magnetic field
,” Phys. Rev. B
84
, 155434
(2011
).30.
S. S.
Krishtopenko
, “Magnetoplasmon excitations from integer-filled Landau levels in narrow-gap quantum wells
,” J. Phys.: Condens. Matter
25
, 365602
(2013
).31.
S. S.
Krishtopenko
, A. V.
Ikonnikov
, M.
Orlita
, Y. G.
Sadofyev
, M.
Goiran
, F.
Teppe
, W.
Knap
, and V. I.
Gavrilenko
, “Effect of electron-electron interaction on cyclotron resonance in high-mobility InAs/AlSb quantum wells
,” J. Appl. Phys.
117
, 112813
(2015
).32.
W.
Kohn
, “Cyclotron resonance and de Haas-van Alphen oscillations of an interacting electron gas
,” Phys. Rev.
123
, 1242
–1244
(1961
).© 2016 Author(s).
2016
Author(s)
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