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Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices. 蔡小明 2013-4-24. 1D hybrid superconductor-semiconductor quantum wires. SOC+ Zeeman field + S-wave pairing. 能谱:.

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slide1

Topological superconductor to Anderson localization transitionin one-dimensional incommensurate lattices

蔡小明

2013-4-24

slide2

1D hybrid superconductor-semiconductor quantum wires

SOC+ Zeeman field + S-wave pairing

能谱:

Fig. A piece of “quantum wire” on the surface of 3-dimensional superconductor.

Toponontraival

1D Kitaev chain:

slide3

Majorana operators:

satisfying

Hamiltonian:

Two special cases

topological trivial

topological nontrivial

Topological nontrivial phase occupies the domain μ<2|w|, Δ≠0.

A. Y. Kitaev, Phys. Usp. 44, 131 (2001).

slide4

Interplay of topo SC and disorder

Topo SC

Anderson localization

increasing disorder

Model:

chemical potential μ=0

incommensurate potential

experimental realization

G. Roati, Nature (London) 453, 895 (2008).

α being an irrational number

slide5

Transition from SC phase to disorder phase (1)

PBC

Corresponding transverse XY model:

correlation function

Transition point:

V=2(t+Δ)

inverse participation ratio (IPR)

u, v the amplitude of the single particle state

extended state

localized state

a finite number

slide6

Finite size analysis

=3.0040±0.0005

slide8

Transition from SC phase to disorder phase (3)

topological invariant

In Majorana operators, the Hamiltonian:

Pfafian:

topological invariant:

M=-1, topo nontrivial

Topological superconductor to Anderson localization phase transition happens at V=2(t+Δ)