# Quantization in chiral higher order topological insulators: circular dichroism and local Chern marker

## TL;DR

This paper investigates the unique quantization properties of chiral higher order topological insulators, revealing how circular dichroism and local Chern markers behave, which helps identify and distinguish these exotic phases.

## Contribution

It introduces novel quantization features of circular dichroism and local Chern markers in chiral HOTIs, highlighting their potential for experimental detection and differentiation from other topological phases.

## Key findings

- Circular dichroism is quantized depending on sample orientation.
- The surface-averaged local Chern marker is nonuniversal for finite surfaces.
- Hinge states contribute to nonuniversal surface properties.

## Abstract

The robust quantization of observables in units of universal constants is a hallmark of topological phases. We show that chiral higher order topological insulators (HOTIs), bulk insulators with chiral hinge states, present two unusual features related to quantization. First, we show that circular dichroism is quantized to an integer or zero depending on the orientation of the sample. This probe locates the hinge states, and can be used to distinguish different types of chiral HOTIs. Second, we find that the average of the local Chern marker over a single surface, an observable related to the surface Hall conductivity known to be quantized in the infinite slab geometry, is nonuniversal for a finite surface. This is due to a nonuniversal contribution of the hinge states, previously unaccounted for, that distinguishes surfaces of chiral HOTIs from Chern insulators. Our findings are relevant to establish higher order topology in systems such as the axion insulator candidate EuIn$_2$As$_2$, and cold atomic realizations.