Fate of topological states and mobility edges in one-dimensional slowly varying incommensurate potentials

Abstract

We investigate the interplay between disorder and superconducting pairing for a one-dimensional $p$-wave superconductor subject to slowly varying incommensurate potentials with mobility edges. With amplitude increments of the incommensurate potentials, the system can undergo a transition from a topological phase to a topologically trivial localized phase. Interestingly, we find that there are four mobility edges in the spectrum when the strength of the incommensurate potential is below a critical threshold, and a novel topologically nontrivial localized phase emerges in a certain region. We reveal this energy-dependent metal-insulator transition by applying several numerical diagnostic techniques, including the inverse participation ratio, the density of states and the Lyapunov exponent. Nowadays, precise control of the background potential and the $p$-wave superfluid can be realized in the ultracold atomic systems, we believe that these novel mobility edges can be observed experimentally.

arXiv comment6 pages, 7 figures

References in corpus (39)

• Topological Insulators
• Topological insulators and superconductors
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Topological superconducting phase in helical Shiba chains
• Three-dimensional localization of ultracold atoms in an optical disordered potential
• Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling
• Three-Dimensional Anderson Localization of Ultracold Matter
• Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films
• Quantized conductance at the Majorana phase transition in a disordered superconducting wire
• Measurement of the mobility edge for 3D Anderson localization
• Majorana Fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials
• Majorana Fermions in superconducting wires: effects of long-range hopping, broken time-reversal symmetry and potential landscapes
• Scattering formula for the topological quantum number of a disordered multi-mode wire
• Two-dimensional p-wave superconducting states with magnetic moments on a conventional s-wave superconductor
• Probability distribution of Majorana end-state energies in disordered wires
• Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
• Interplay of disorder and interaction in Majorana quantum wires
• Fusion rules and vortices in $p_x+i{p}_y$ superconductors
• Topological Yu-Shiba-Rusinov chain from spin-orbit coupling
• Phase diagram of a non-Abelian Aubry-André-Harper model with $p$-wave superfluidity
• Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
• Localization and delocalization in dirty superconducting wires
• Localization in disordered superconducting wires with broken spin-rotation symmetry
• Anderson Localization of cold atomic gases with effective spin-orbit interaction in a quasiperiodic optical lattice
• Realizing one-dimensional topological superfluids with ultracold atomic gases
• Bound states of a ferromagnetic wire in a superconductor
• Majorana bound states in a disordered quantum dot chain
• Calculation of the conductance of a graphene sheet using the Chalker-Coddington network model
• Localization and mobility edges in the off-diagonal quasiperiodic model with slowly varying potentials
• Noise Correlation Scalings: Revisiting the Quantum Phase Transition in Incommensurate Lattices with Hard-Core Bosons
• Phase diagram of the off-diagonal Aubry-André model

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• Topological phase transition in the quasiperiodic disordered Su-Schriffer-Heeger chain
• Single-Particle Mobility Edge without Disorder
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Quantum transport in a one-dimensional quasicrystal with mobility edges
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals