# Distinguishing trivial and topological quadrupolar insulators by Wannier-Stark ladders

## TL;DR

This paper proposes a method to distinguish trivial and topological quadrupolar insulators by analyzing their Wannier-Stark ladder spectra under an electric field, aiding in the characterization of higher-order topological phases.

## Contribution

It introduces a theoretical approach using Wannier-Stark ladders to identify topological phases in quadrupolar insulators, providing a new diagnostic tool.

## Key findings

- Wannier-Stark ladders are quantized in topological phases
- Energy spectrum differences reveal topological vs trivial phases
- Method applicable to light and matter systems

## Abstract

I study theoretically quadrupolar topological insulators under applied static electric field rotated along the crystal axis. I demonstrate, that the energy spectrum of this structure is a Wannier-Stark ladder that is quantized and directly distinguishes between the topological phase, possessing localized corner states, and the trivial phase, lacking the corner states. These results may find applications in the characterization of rapidly emerging higher-order topological phases of light and matter.