Topological finite size effect in one-dimensional chiral symmetric systems

TL;DR

This paper investigates how finite size and disorder influence topological properties in one-dimensional chiral symmetric systems, proposing a new bulk conductivity criterion for better topology characterization in real-world applications.

Contribution

It introduces a novel criterion based on bulk conductivity to characterize finite topological systems, validated through analytical and numerical analysis of SSH models.

Findings

Bulk conductivity effectively indicates topological phases in finite systems.

Finite size and disorder impact topological invariants and edge modes.

The approach aids experimental topology detection in intermediate-scale systems.

Abstract

Topological phases of matter have been widely studied for their robustness against impurities and disorder. The broad applicability of topological materials relies on the reliable transition from idealized, mathematically perfect models to finite, real-world implementations. In this paper, we explore the effects of finite size and disorders on topological properties. We propose a new criterion for characterizing finite topological systems based on the bulk conductivity of topological edge modes. We analyze the behavior of bulk conductivity and real space topological invariants both analytically and numerically for the family of SSH models. We show that our approach offers practical insights for topology determination in contemporary intermediate scale experimental applications.