Topological Superconductor to Anderson Localization Transition in One-Dimensional Incommensurate Lattices

2012/08/31 by Xiaoming Cai, Li-Jun Lang, Shu Chen +1 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Condensed matter physics #Fermion #Invariant (physics) #MAJORANA #Mathematics #Phase (matter) #Phase transition #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Superconductivity #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.str-el

paper · pdf · doi:10.1103/physrevlett.110.176403

published as Phys. Rev. Lett. 110, 176403 (2013) · 5 + 4 pages, 5 +2 figures, version appeared in PRL, supplementary material included

openalex publication_date 2013/04/26 · arxiv created 2013/05/01 · arxiv updated 2015/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the competition of disorder and superconductivity for a one-dimensional p-wave superconductor in incommensurate potentials. With the increase in the strength of the incommensurate potential, the system undergoes a transition from a topological superconducting phase to a topologically trivial localized phase. The phase boundary is determined both numerically and analytically from various aspects and the topological superconducting phase is characterized by the presence of Majorana edge fermions in the system with open boundary conditions. We also calculate the topological Z2 invariant of the bulk system and find it can be used to distinguish the different topological phases even for a disordered system.

Citations

• Localization in disordered superconducting wires with broken spin-rotation symmetry
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Delocalization and Heisenberg's uncertainty relation
• Fusion rules and vortices inpx+ipysuperconductors
• Helical Liquids and Majorana Bound States in Quantum Wires
• Electrons in disordered systems and the theory of localization
• Anomalous Zero-Bias Conductance Peak in a Nb–InSb Nanowire–Nb Hybrid Device
• Search for Majorana Fermions in Superconductors
• Two soluble models of an antiferromagnetic chain
• Unpaired Majorana fermions in quantum wires

Cited by

• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Divergent density of states and non-analytic Lyapunov exponent in one-dimensional slowly varying systems
• Almost mobility edges and the existence of critical regions in one-dimensional quasiperiodic lattices
• Shuttling Majorana zero modes in disordered and noisy topological superconductors
• Reentrant localization transition induced by a composite potential

Related

• Localization and Topology in Noncentrosymmetric Superconductors with Disorder
• Topological Superconductors in One-Dimensional Mosaic Lattices
• Topology and quantum phases of low dimensional fermionic systems
• Mapping Topology-Localization Phase Diagram with Quasiperiodic Disorder Using a Programmable Superconducting Simulator
• Fate of Majorana zero modes by a modified real-space-Pfaffian method and mobility edges in a one-dimensional quasiperiodic lattice