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

TL;DR

This paper explores how slowly varying incommensurate potentials affect topological states and mobility edges in a one-dimensional p-wave superconductor, revealing multiple mobility edges and a new topologically nontrivial localized phase.

Contribution

It uncovers the existence of four mobility edges and a novel topologically nontrivial localized phase in a 1D p-wave superconductor with incommensurate potentials, advancing understanding of disorder effects.

Findings

Four mobility edges identified below a critical potential strength.

Emergence of a topologically nontrivial localized phase.

Energy-dependent metal-insulator transition demonstrated.

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.