Localization transitions and mobility edges in quasiperiodic ladder

TL;DR

This paper studies localization transitions and mobility edges in a quasiperiodic ladder system, revealing conditions for mobility edge appearance and proposing an experimentally detectable dynamic method for its identification.

Contribution

It introduces a quasiperiodic ladder model with mobility edges and a dynamic detection method, expanding understanding of localization in complex systems.

Findings

Mobility edges appear in asymmetric quasiperiodic ladders.

A moiré superlattice system supports mobility edges.

Dynamic measurement can detect mobility edges experimentally.

Abstract

We investigate localization properties in a two-coupled uniform chains with quasiperiodic modulation on interchain coupling strength. We demonstrate that this ladder is equivalent to a Aubry-Andre (AA) chain when two legs are symmetric. Analytical and numerical results indicate the appearance of mobility edges for asymmetric ladder. We also propose an easily engineered quasiperiodic ladder system which is a moir\'{e} superlattice system consisting of two-coupled uniform chains. An irrational lattice constant difference results in quasiperiodic structure. Numerical simulations show that such a system supports mobility edge. Additionally, we find that the mobility edge can be detected by a dynamic method, which bases on the measurement of surviving probability in the presence of a single imaginary negative potential as a leakage. The result provides insightful information about the localization transitions and mobility edge in experiment.