Title: BACKSCATTERING
1BACKSCATTERING OF EDGE ELECTRONS IN A STRIP OF
2D TOPOLOGICAL INSULATOR L.Magarill, M.
Entin Institute of Semiconductor Physics SB
RAS, Novosibirsk, Russia
2Edge states in a strip of 2D topological insulator
z
y
x
S
v
HgTe
S
v
3Outline
1.Edge states in 2D topological insulator 2.
Motivation 3. Construction of edge states in a
strip 4. Edge state Hamiltonian 5. Scattering
between edges in classical model 6. Specific
kinds of scattering mechanisms impurities,
phonons, edge irragularities 7. Forward phonon
scattering as a dephasing mechanism 8. Low
temperature localization of edge states in a
strip 9. Bulk 2D conductivity
4Motivation In a topological insulator current
flows along 1D edges
Hence
At the same time the theory of localization
stated that if length of 1D system
?
5Valence-band Hamiltonian of 2D HgTe
k- is in-plane momentum A,B,D are band
parameters 2M is a 2D gap
6Edge states
2D states
Edge states
7Two edges
z
y
x
v
L
HgTe
v
L
Gap
8Edge-state Hamiltonian
System with impurities
9Impurity scattering kinetic equation
Electric field
Backscattering rate
Impurity potential
x
v
10Conductance of finite strip
Long system
Ballistic case
11Edge imperfectness scattering
12Phonon scattering elastic approximation
13Localization
14Single impurity
15Multiple impurities
x
v
16Transition coefficient
Conductance
Localization length
17Localization length
18Resistance
19Phase coherence time
Forward scattering
Kinetic regime
Localization regime
20Bulk conductivity of 2D topological insulator
Edge states in Dirac model
21Random
S
D
D
S
22Resistivity
23- Conclusions
- Interedge scattering between edge states
determines the conductivity of - 2D topological insulator strip.
- Interedge scattering exponentially decay with the
strip width. - Intraedge inelastic scattering determines the
phase decoherence and - kinetic equation applicability.
- At low temperature the localization of edge
states in a strip occurs. - Random fluctuations of the gap sign determine the
network of internal edge states. - Hoppings between these edges yield 2D
conductivity.
24Thank you for attention
25Nonlocal resistance