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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.
Co-authors:
•
•
•
•
E.B.Olshanetsky
O.A.Shegai
D.A.Kozlov
G.M.Gusev
•
(Universidade de S˜ao Paulo, Brazil)
Measurements
• K. Dantscher
• C. Zot
• S.D.Ganichev
•
(Regensburg University)
• N.N. Mikhailov
• S.A. Dvoretsky
MBE growth
Semiconductors with direct and inverted band structure
Inverted band structure
Direct band structure
J=l+s;
EC ; s (l=0)
J=1/2;
j=±1/2
EC ; p (l=1)
J=3/2;j = ±1/2
g - 0.35 eV
EV ; p (l=1)
J=3/2;j = ±3/2
EV ; p (l=1)
g≈1.5eV
k
CdTe
J=3/2;
j=±3/2;
j=±1/2
EV ; s (l=0)
J=1/2
J=1/2;
j=±1/2;
EV ; p (l=1)
J=1/2
Ve ~
Z2(e2/h)
k
HgTe
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
2D топологический изолятор в HgTe
квантовых ямах (dw = 7-9 nm)
H1 j = ±3/2
0
W
Gap = (10 – 50) meV
E1 j = ±1/2
0
W
with the gap
Energy spectrum
(O.E Raichev, Phys. Rev.B 85, 045310 (2012))
DoS
Density of states
Ev
DP
Ec
E
Topological protection means no back-scattering!
Spin is uniquely connected with momentum due to time resersal symmetry (TRS)
s
|1>
p
|2> p
s
<1|2> = 0 if spin dependent interaction is
absent
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
The lower 1D single-mode wire
In a diffusive case (max{lu, ll} << L)
G = Gu + Gl = [(lu + ll)/L]e2/h =
Experiment (Wurzburg group): ballistic case
HgTe quantum well field effect transistor
Temperature dependence
Nonlocal transport
Rnl ≈ 2·10-3ρxx для L/W = 2 и Rnl ≈ 10-10ρxx для L/W = 7
Typical experiment
Transition 2D TI – 2D Dirac metal induced
by in-plain magnetic field
Four-terminal local RI=1,4;V=2,3 (black)
and nonlocal RI=6,2;V=5,3 (red dashes)
resistances as a function of the gate
voltage at T = 4.2 K and B = 0.
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) :
Δσ(B)/σ = - α|B|;
α strongly depends on disorder strength Γ
Our experiments are in agreement with the case of a
small disorder Γ < Eg
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)
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, I=10-9 A. The top
panel shows schematics view of the
sample.
Conclusion: no one-dimensional
localization.
Glasman et al model
Result: G < 2e2/h only at T>0.
So one should observe no localization
and significant temperature dependence.
It contradicts the experiment in which
there is no significant R(T) dependence.
Terahertz photoconductivity experiment
2D TI terahertz photoconductivity origin
2D topological insulator with complicate
bulk energy spectrum: 14 nm HgTe QW
W
Γ ~ (∆dW/dW)3
Experiment
70μm
250μm
100μm
Temperature dependence of local and nonlocal
resistance at CNP
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