2D Topological insulator in HgTe quantum wells

1

• 2D Topological insulator in HgTe quantum wells
• Z.D. Kvon
• Institute of Semiconductor Physics, Novosibirsk,
  Russia
• 1. Introduction. HgTe quantum wells.
• 2. 2D topological insulator in HgTe quantum
  wells.
• 3. Edge current transport. Ballistics and
  diffusion.
• 4. Terahertz photoconductivity.
• 5. New topological insulator in HgTe QW.

2
Co-authors

• E.B.Olshanetsky
• O.A.Shegai
• D.A.Kozlov
• G.M.Gusev
• (Universidade de Sao Paulo, Brazil)
• K. Dantscher
• C. Zot
• S.D.Ganichev
• (Regensburg University)
• N.N. Mikhailov
• S.A. Dvoretsky

Measurements MBE growth
3
Semiconductors with direct and inverted band
structure
EV p (l1)
Ve Z2(e2/h)
CdTe
HgTe
4
Energy spectrum in HgTe quantum well
(M.I.Dyakonov and A.V.Khaetskii, JETP, 55, 917
(1982), Y.Lin-Liu, L.Sham, PRB, 32, 5561 (1985)
L.G.Gerchikov and A.V.Subashiev, PSS(b), 160,
443(1990), B.Bernevig et al, Science, 314, 1757
(2006), E.G.Novik et al. PRB, 83, 193304(2011)),
O.E.Raichev, PRB, 85, 045310 (2012))

dw, nm
5
2D ?????????????? ???????? ? HgTe ????????? ????
(dw 7-9 nm)
H1
j 3/2
0
W
Gap (10 50) meV
E1
j 1/2
0
W
with the gap
6
Energy spectrum (O.E Raichev, Phys. Rev.B 85,
045310 (2012))
Density of states
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Topological protection means no
back-scattering!Spin is uniquely connected with
momentum due to time resersal symmetry (TRS)

• 1gt 2gt
• lt12gt 0 if spin dependent interaction is
  absent

s
p
p
s
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Experimental consequences for 2D TI two probes
conductance

• The upper 1D single-mode wire

In a ballistic case G Gu Gl I/(µleft
µright) e2/h e2/h 2e2/h
insulator
L
In a diffusive case (maxlu, ll ltlt L) G Gu
Gl (lu ll)/Le2/h
The lower 1D single-mode wire
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Experiment (Wurzburg group) ballistic case
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HgTe quantum well field effect transistor
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Temperature dependence
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Nonlocal transport
Rnl 2?10-3?xx ??? L/W 2 ? Rnl 10-10?xx
??? L/W 7
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Typical experiment
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Transition 2D TI 2D Dirac metal induced by
in-plain magnetic field
Four-terminal local RI1,4V2,3 (black) and
nonlocal RI6,2V5,3 (red dashes) resistances as
a function of the gate voltage at T 4.2 K and B
0.
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Linear positive magnetoresistance caused by the
breaking of the TRS in a normal magnetic field
According to the theory (J. Maciejko, X-L. Qi,
and S-C. Zhang, Phys. Rev. B 82, 155310 (2010)
?s(B)/s - aB a strongly depends on
disorder strength G Our experiments are in
agreement with the case of a small disorder G lt
Eg
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Edge current state in 2DTI as single-mode long
disorder wire
Theoretical picture (Mirlin, Gornyi and
Polyakov, PRB, 75, 085421 (2007)
Experiment with V-grooves single-mode wires
E.Levy et al, PRB, 85, 045315 (2012)
T(K)
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Low temperature behavior of HgTe based 2D TI
The resistance R one of the samples of The sample
as a function of the temperature at charge
neutrality point (Vg VCNP) 0 measured by
various voltage probes in the temperature interval
(4-0.3) K, I10-9 A. The top panel shows
schematics view of the sample.
Conclusion no one-dimensional localization.
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Glasman et al model
Result G lt 2e2/h only at Tgt0. So one should
observe no localization and significant
temperature dependence. It contradicts the
experiment in which there is no significant R(T)
dependence.
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Terahertz photoconductivity experiment
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2D TI terahertz photoconductivity origin
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2D topological insulator with complicate bulk
energy spectrum 14 nm HgTe QW
W
G (?dW/dW)3
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Experiment
250µm
100µm
70µm
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Temperature dependence of local and nonlocal
resistance at CNP