Anderson localization via Peierls phase modulation

TL;DR

This paper explores how modulating Peierls phases in a two-leg ladder system under magnetic fields can induce localization or delocalization of eigenstates, revealing a phase transition controlled by phase modulation.

Contribution

It introduces a novel mechanism for localization control through quasiperiodic Peierls phase modulation, including phase diagram construction and semiclassical analysis.

Findings

Random Peierls phases cause complete localization.

Quasiperiodic phase modulation induces a transition from delocalized to localized states.

Phase diagram shows regions of mixed phases separated by localization transitions.

Abstract

We investigate a two leg ladder system subjected to an external magnetic field. In the absence of a magnetic field, the system is described by a clean tight binding model, with no disorder in either the onsite potential or the hopping amplitudes. The effect of magnetic field in this system is studied by introducing the Peierls phases in the hopping amplitudes along a leg (appropriate when the Landau gauge is chosen). For a uniform magnetic field, characterized by a constant Peierls phase, we find that all eigenstates remain delocalized. In contrast, random Peierls phases, representing a random magnetic field, lead to complete localization of the eigenstates. We further show that a quasiperiodic modulation of the Peierls phase can drive a transition from a fully delocalized to a fully localized phase upon tuning the quasiperiodicity. For a two parameter quasiperiodic Peierls phase, varying analogously to a generalized Aubry Andre type potential, we construct the phase diagram of the system. The phase diagram exhibits regions of delocalized and localized phases, separated by intermediate regimes of mixed phase. We also perform a semiclassical analysis that qualitatively yields a similar phase diagram, capturing the localization transition. Our results demonstrate a mechanism for controlling transport properties via the Peierls phase engineering.