Mobility Crossover in Two-Dimensional Berry Crystals

TL;DR

This paper investigates the spectral and localization properties of a two-dimensional Berry crystal, revealing a mobility crossover from extended to localized states and highlighting the unique presence of critical states across a broad energy regime.

Contribution

It introduces the concept of a 'mobility crossover' in 2D Berry crystals, showing extended critical states and their evolution with potential strength, contrasting with traditional quasicrystals.

Findings

Berry crystal exhibits Anderson localization and critical states.

Critical states form a broad regime, not just at sharp mobility edges.

Transition from extended to localized states occurs as potential strength increases.

Abstract

A Berry crystal is a random superposition of N plane waves of equal amplitude and fixed wavevector magnitude, propagating in different directions. Using numerical simulations of wavepacket dynamics, spectral analysis based on autocorrelation functions, and scaling of Inverse Participation Ratio, the nature of eigenstates across the energy spectrum of a two-dimensional Berry crystal is characterized. It exhibits Anderson localization and critical (extended but non-ergodic) states, reminiscent of quasicrystals, which sit in the middle ground between periodic and disordered systems and can host critical states. However, in contrast to quasicrystals that display sharp mobility edges separating extended and localized phases, the Berry crystal exhibits an extended regimes of critical states. We name this a "mobility crossover". At weak potential strength, low-energy states are extended while higher-energy states near the backscattering momentum are critical. As the potential strength increases to become comparable with the recoil energy, these critical states evolve into localized states, yielding a transition from extended non-ergodic to localized behavior near the backscattering momentum. An estimate for the boundaries of ergodic extended regimes is given by the mapping onto an effective Anderson model on a Bethe Lattice. The results shed light on the relation between backscattering and Anderson localization in continuous two-dimensional aperiodic systems.