Two-Dimensional Electron Gas with Cold Atoms in Non-Abelian Gauge Potentials

TL;DR

This paper investigates the complex spectral and localization phenomena of two-dimensional electron gases in non-Abelian gauge fields created by cold atoms, revealing novel band structures, relativistic effects, and unique transport properties.

Contribution

It introduces a continuum and lattice model for 2DEGs under non-Abelian gauge potentials, uncovering new spectral features like Landau band splitting and the 'moth' spectrum, and explores their impact on localization and transport.

Findings

Landau levels split into bands depending on transverse momentum

The spectrum forms a 'moth'-like continuum similar to Hofstadter butterfly

Localization can be induced or suppressed by tuning quasimomentum

Abstract

Motivated by the possibility of creating non-Abelian fields using cold atoms in optical lattices, we explore the richness and complexity of non-interacting two-dimensional electron gases (2DEGs) in a lattice, subjected to such fields. In the continuum limit, a non-Abelian system characterized by a two-component "magnetic flux" describes a harmonic oscillator existing in two different charge states (mimicking a particle-hole pair) where the coupling between the states is determined by the non-Abelian parameter, namely the difference between the two components of the "magnetic flux." A key feature of the non-Abelian system is a splitting of the Landau energy levels, which broaden into bands, as the spectrum depends explicitly on the transverse momentum. These Landau bands result in a coarse-grained "moth," a continuum version of the generalized Hofstadter butterfly. Furthermore, the bands overlap, leading to effective relativistic effects. Importantly, similar features also characterize the corresponding two-dimensional lattice problem when at least one of the components of the magnetic flux is an irrational number. The lattice system with two competing "magnetic fluxes" penetrating the unit cell provides a rich environment in which to study localization phenomena. Some unique aspects of the transport properties of the non-Abelian system are the possibility of inducing localization by varying the quasimomentum, and the absence of localization of certain zero-energy states exhibiting a linear energy-momentum relation. Furthermore, non-Abelian systems provide an interesting localization scenario where the localization transition is accompanied by a transition from relativistic to non-relativistic theory.