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.

6 pages, 7 figures

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Cited by in corpus (6)

• Fate of Majorana zero modes, critical states and non-conventional real-complex transition in non-Hermitian quasiperiodic lattices
• Ring Structure in the Complex Plane: A Fingerprint of non-Hermitian Mobility Edge
• 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