2D Topological insulator in HgTe quantum wells Z.D. Kvon

2D Topological insulator in HgTe quantum wells ZD 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

bull EBOlshanetskybull OAShegaibull DAKozlovbull GMGusev bull (Universidade de S˜ao Paulo Brazil)

bull K Dantscherbull C Zotbull SDGanichevbull (Regensburg University)

bull NN Mikhailovbull SA Dvoretsky

Measurements

MBE growth

Semiconductors with direct and inverted band structure

k

EV p (l=1)

EC s (l=0)

J=12j=plusmn12

J=32j=plusmn32j=plusmn12

J=12j=plusmn12

Direct band structure

J=l+s

gasymp15eV

k

EC p (l=1)

J=32j = plusmn12

EV p (l=1)

J=32j = plusmn32

EV s (l=0)

J=12

EV p (l=1)

J=12

Inverted band structure

g - 035 eV

CdTe HgTeVe ~ Z2(e2h)

Energy spectrum in HgTe quantum well

dw nm

(MIDyakonov and AVKhaetskii JETP 55 917 (1982) YLin-Liu LSham PRB 32 5561 (1985) LGGerchikov and AVSubashiev PSS(b) 160 443(1990) BBernevig et al Science 314 1757 (2006) EGNovik et al PRB 83 193304(2011)) OERaichev PRB 85 045310 (2012))

2D топологический изолятор в HgTe квантовых ямах (dw = 7-9 nm)

H1

E1

Gap = (10 ndash 50) meV

0 W

0W

with the gap

j = plusmn32

j = plusmn12

Energy spectrum (OE Raichev Phys RevB 85 045310 (2012))

DP Ec

DoS

E

Ev

Density of states

|1gt |2gt

lt1|2gt = 0 if spin dependent interaction is absent

Topological protection means no back-scattering

Spin is uniquely connected with momentum due to time resersal symmetry (TRS)

p

s p

s

Experimental consequences for 2D TI two probes conductance

bull The upper 1D single-mode wire

The lower 1D single-mode wire

In a ballistic caseG = Gu + Gl = I(μleft ndash μright) =e2h + e2h = 2e2h

In a diffusive case (maxlu ll ltlt L)G = Gu + Gl = [(lu + ll)L]e2h =

insulatorL

Experiment (Wurzburg group) ballistic case

HgTe quantum well field effect transistor

Temperature dependence

Nonlocal transport

Rnl asymp 210-3ρxx для LW = 2 и Rnl asymp 10-10ρxx для LW = 7

Typical experiment

Transition 2D TI ndash 2D Dirac metal induced by in-plain magnetic field

Four-terminal local RI=14V=23 (black)and nonlocal RI=62V=53 (red dashes) resistances as a function of the gate voltage at T = 42 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 ΓOur experiments are in agreement with the case of a small disorder Γ lt 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 ELevy et al PRB 85 045315 (2012)

T(K)

Low temperature behavior of HgTe based 2D TI

The resistance R one of the samples ofThe sample as a function of thetemperature at charge neutrality point(Vg ndash VCNP) = 0 measured by variousvoltage probes in the temperatureinterval (4-03) K I=10-9 A The toppanel shows schematics view of thesample

Conclusion no one-dimensional localization

Glasman et al model

Result G lt 2e2h only at Tgt0So one should observe no localizationand significant temperature dependenceIt 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 ~ (∆dWdW)3

Experiment

70μ

m

250μm 100μm

Temperature dependence of local and nonlocal resistance at CNP

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Co-authors

bull EBOlshanetskybull OAShegaibull DAKozlovbull GMGusev bull (Universidade de S˜ao Paulo Brazil)

bull K Dantscherbull C Zotbull SDGanichevbull (Regensburg University)

bull NN Mikhailovbull SA Dvoretsky

Measurements

MBE growth


k

EV p (l=1)

EC s (l=0)

J=12j=plusmn12


J=12j=plusmn12


J=l+s

gasymp15eV

k

EC p (l=1)

J=32j = plusmn12

EV p (l=1)

J=32j = plusmn32

EV s (l=0)

J=12

EV p (l=1)

J=12


g - 035 eV



dw nm



H1

E1


0 W

0W

with the gap

j = plusmn32

j = plusmn12


DP Ec

DoS

E

Ev

Density of states

|1gt |2gt




p

s p

s






insulatorL




Nonlocal transport


Typical experiment









T(K)




Glasman et al model





W

Γ ~ (∆dWdW)3

Experiment

70μ

m

250μm 100μm


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k

EV p (l=1)

EC s (l=0)

J=12j=plusmn12


J=12j=plusmn12


J=l+s

gasymp15eV

k

EC p (l=1)

J=32j = plusmn12

EV p (l=1)

J=32j = plusmn32

EV s (l=0)

J=12

EV p (l=1)

J=12


g - 035 eV



dw nm



H1

E1


0 W

0W

with the gap

j = plusmn32

j = plusmn12


DP Ec

DoS

E

Ev

Density of states

|1gt |2gt




p

s p

s






insulatorL




Nonlocal transport


Typical experiment









T(K)




Glasman et al model





W

Γ ~ (∆dWdW)3

Experiment

70μ

m

250μm 100μm


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dw nm



H1

E1


0 W

0W

with the gap

j = plusmn32

j = plusmn12


DP Ec

DoS

E

Ev

Density of states

|1gt |2gt




p

s p

s






insulatorL




Nonlocal transport


Typical experiment









T(K)




Glasman et al model





W

Γ ~ (∆dWdW)3

Experiment

70μ

m

250μm 100μm


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H1

E1


0 W

0W

with the gap

j = plusmn32

j = plusmn12


DP Ec

DoS

E

Ev

Density of states

|1gt |2gt




p

s p

s






insulatorL




Nonlocal transport


Typical experiment









T(K)




Glasman et al model





W

Γ ~ (∆dWdW)3

Experiment

70μ

m

250μm 100μm


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DP Ec

DoS

E

Ev

Density of states

|1gt |2gt




p

s p

s






insulatorL




Nonlocal transport


Typical experiment









T(K)




Glasman et al model





W

Γ ~ (∆dWdW)3

Experiment

70μ

m

250μm 100μm


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|1gt |2gt




p

s p

s






insulatorL




Nonlocal transport


Typical experiment









T(K)




Glasman et al model





W

Γ ~ (∆dWdW)3

Experiment

70μ

m

250μm 100μm


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insulatorL




Nonlocal transport


Typical experiment









T(K)




Glasman et al model





W

Γ ~ (∆dWdW)3

Experiment

70μ

m

250μm 100μm


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Nonlocal transport


Typical experiment









T(K)




Glasman et al model





W

Γ ~ (∆dWdW)3

Experiment

70μ

m

250μm 100μm


Slide 1

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Typical experiment









T(K)




Glasman et al model





W

Γ ~ (∆dWdW)3

Experiment

70μ

m

250μm 100μm


Slide 1

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T(K)




Glasman et al model





W

Γ ~ (∆dWdW)3

Experiment

70μ

m

250μm 100μm


Slide 1

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Glasman et al model





W

Γ ~ (∆dWdW)3

Experiment

70μ

m

250μm 100μm


Slide 1

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W

Γ ~ (∆dWdW)3

Experiment

70μ

m

250μm 100μm


Slide 1

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Experiment

70μ

m

250μm 100μm


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2D Topological insulator in HgTe quantum wells Z.D. Kvon

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