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蔡小明 2013-4-24

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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蔡小明 2013-4-24

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  1. Topological superconductor to Anderson localization transitionin one-dimensional incommensurate lattices 蔡小明 2013-4-24

  2. 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:

  3. 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).

  4. 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

  5. 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

  6. Finite size analysis =3.0040±0.0005

  7. Transition from SC phase to disorder phase (2) OPC

  8. 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)

  9. THANKS!

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