# Fractional corner charges in spin-orbit coupled crystals

## TL;DR

This paper classifies and characterizes fractional corner charges in two-dimensional spin-orbit coupled insulators protected by symmetries, linking corner charge configurations to bulk topology using symmetry indicators and Wilson loops.

## Contribution

It provides a comprehensive classification of corner charge configurations for all point groups and formulas for calculating corner charges from Bloch wavefunctions.

## Key findings

- Corner charges are quantized and topologically stable under symmetry preservation.
- Density functional theory calculations support the theoretical predictions.
- Materials like arsenic and antimony monolayers can exhibit distinct topological phases.

## Abstract

We study two-dimensional spinful insulating phases of matter that are protected by time-reversal and crystalline symmetries. To characterize these phases we employ the concept of corner charge fractionalization: Corners can carry charges that are fractions of even multiples of the electric charge. The charges are quantized and topologically stable as long as all symmetries are preserved. We classify the different corner charge configurations for all point groups, and match them with the corresponding bulk topology. For this we employ symmetry indicators and (nested) Wilson loop invariants. We provide formulas that allow for a convenient calculation of the corner charge from Bloch wavefunctions and illustrate our results using the example of arsenic and antimony monolayers. Depending on the degree of structural buckling, these materials can exhibit two distinct obstructed atomic limits. We present density functional theory calculations for open flakes to support our findings.