# Finite-size effects in non-Hermitian topological systems

## TL;DR

This paper explores how finite-size effects influence non-Hermitian topological systems, revealing modifications in localization and energy gaps in 1D and 2D models through analytical and numerical methods.

## Contribution

It provides a systematic analysis of finite-size effects in non-Hermitian topological models, highlighting how intra-cell hoppings and on-site potentials affect energy gaps and localization.

## Key findings

- Non-Hermitian intra-cell hoppings modify localization lengths and cause oscillating finite-size energy gaps.
- Imaginary staggered potentials change end-state energies but not localization lengths.
- Finite-size effects in 2D Chern insulators show similar phenomena as in 1D models.

## Abstract

We systematically investigate the finite-size effects in non-Hermitian one-dimensional (1D) Su-Schrieffer-Heeger (SSH) and two-dimensional (2D) Chern insulator models. Using a combination of analytical and numerical calculations, we show that the non-Hermitian intra-cell hoppings in the SSH model can modify the localization lengths of bulk and end states, giving rise to a complex finite-size energy gap that exhibits an oscillating exponential decay as the chain length grows. However, the imaginary staggered on-site potentials in the SSH model only change the end-state energy, leaving the localization lengths of the system unchanged. In this case, the finite-size energy gap can undergo a transition from real values to imaginary values. We observed similar phenomena for the finite-size effect in 2D Chern insulator systems.