# Chirality polarizations and spectral bulk-boundary correspondence

## TL;DR

This paper extends the theory of electric polarization to chirality polarizations, establishing a spectral bulk-boundary correspondence in chiral symmetric systems through both physical and formal proofs.

## Contribution

It introduces the concept of chirality polarizations and proves a generalized bulk-boundary correspondence for complex frequencies in chiral symmetric systems.

## Key findings

- Proves the spectral bulk-boundary correspondence using Wannier functions.
- Highlights similarities and differences between electric and chirality polarizations.
- Provides a physically transparent and formal proof of the correspondence.

## Abstract

Surface physics dominated by bulk properties has been one of the central interests in modern condensed matter physics, from electric polarization to bulk-boundary correspondence of topological insulators and superconductors. Here, we extend theory of electric polarization to chirality polarizations, that is, surface charges corresponding to local antisymmetries characterized as a bulk property. Using the notion of chirality polarizations, we prove the recently proposed spectral bulk-boundary correspondence, a generalization of bulk-boundary correspondence in chiral symmetric systems into complex frequencies. We show a physically transparent proof via Wannier functions and a formal proof by considering the change of surface chirality charges, highlighting the similarities and the differences between electric polarization and chirality polarizations.