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.
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2D Topological insulator in HgTe quantum wells Z.D. Kvon
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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))
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
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))
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
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))
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
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))
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
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
|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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
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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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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Slide 23
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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Slide 23
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
Slide 1
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Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
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
Slide 1
Slide 2
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Slide 13
Slide 14
Slide 15
Slide 16
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Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
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
Slide 1
Slide 2
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Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
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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Slide 22
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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 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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Slide 23
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
Slide 1
Slide 2
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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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Slide 23
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
Slide 1
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Slide 23
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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Slide 23
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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Experiment
70μ
m
250μm 100μm
Temperature dependence of local and nonlocal resistance at CNP
Slide 1
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Temperature dependence of local and nonlocal resistance at CNP