Anisotropic Anderson localization in higher-dimensional nonreciprocal lattices

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.