Anisotropic Anderson localization in higher-dimensional nonreciprocal lattices

TL;DR

This paper explores how nonreciprocity affects Anderson localization in higher-dimensional lattices, revealing anisotropic hybrid modes and transitions between skin and Anderson localized states, with implications for wave phenomena in complex systems.

Contribution

It introduces the concept of anisotropic hybrid modes in nonreciprocal lattices and maps out mobility edges and phase transitions in higher dimensions, extending understanding of localization phenomena.

Findings

Identification of anisotropic hybrid modes with skin and Anderson localization

Mapping of mobility edges and reentrant ALM-HM-ALM transitions

Demonstration of skin-Anderson transitions in infinite-dimensional Bethe lattice

Abstract

Nonreciprocity breaks the symmetry between forward and backward propagation, giving rise to a range of peculiar wave phenomena. In this work, we investigate Anderson localization in higher-dimensional nonreciprocal lattices. Focusing on the two-dimensional Hatano-Nelson model, we uncover anisotropic hybrid modes (HMs) that exhibit skin localization along one direction and Anderson localization along the other. We determine the Anderson transition along different directions via the transfer matrix approach and finite-size scaling of Lyapunov exponents. This allows us to map out mobility edges that separate HMs from normal skin modes and Anderson localized modes (ALMs), revealing an ALM-HM-ALM reentrant transition. Our analysis extends to arbitrary dimensions, and we demonstrate the existence of skin-Anderson transitions on the infinite-dimensional nonreciprocal Bethe lattice using the forward-scattering approximation.