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

2. Fig. A piece of “quantum wire” on the surface of 3- dimensional superconductor. SOC+ Zeeman field + S-wave pairing 1D hybrid superconductor-semiconductor quantum wires 1D Kitaev chain: 能谱： Topo nontraival

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. chemical potential μ=0 Interplay of topo SC and disorder increasing disorder Topo SC Anderson localization Model: incommensurate potential α being an irrational number experimental realization G. Roati, Nature (London) 453, 895 (2008).

5. Transition from SC phase to disorder phase (1) PBC Corresponding transverse XY model: correlation function inverse participation ratio (IPR) u, v the amplitude of the single particle state extended state localized state a finite number Transition point: V=2(t+Δ)

6. Finite size analysis

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

8. In Majorana operators, the Hamiltonian: M=-1, topo nontrivial Transition from SC phase to disorder phase (3) Topological superconductor to Anderson localization phase transition happens at V=2(t+Δ) Pfafian: