# Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices

## TL;DR

This paper investigates how non-Hermitian skin effects interact with Anderson localization in non-reciprocal quasiperiodic lattices, revealing a topological transition characterized by a winding number and demonstrating experimental realizability with passive electronic circuits.

## Contribution

It provides an exact proof of a rescaled transition point in non-reciprocal Aubry-André models and links the interplay of NHSE and localization to a topological invariant, with practical circuit implementation.

## Key findings

- Identifies a topological transition characterized by a winding number.
- Shows non-reciprocity induces asymmetric localized states.
- Demonstrates experimental realization using passive RLC circuits.

## Abstract

Non-Hermiticity from non-reciprocal hoppings has been shown recently to demonstrate the non-Hermitian skin effect (NHSE) under open boundary conditions (OBCs). Here we study the interplay of this effect and the Anderson localization in a \textit{non-reciprocal} quasiperiodic lattice, dubbed non-reciprocal Aubry-Andr\'{e} model, and a \textit{rescaled} transition point is exactly proved. The non-reciprocity can induce not only the NHSE, but also the asymmetry in localized states with two Lyapunov exponents for both sides. Meanwhile, this transition is also topological, characterized by a winding number associated with the complex eigenenergies under periodic boundary conditions (PBCs), establishing a \textit{bulk-bulk} correspondence. This interplay can be realized by an elaborately designed electronic circuit with only linear passive RLC devices instead of elusive non-reciprocal ones, where the transport of a continuous wave undergoes a transition between insulating and amplifying. This initiative scheme can be immediately applied in experiments to other non-reciprocal models, and will definitely inspires the study of interplay of NHSEs and more other quantum/topological phenomena.