# High-Order Multipole Radiation from Quantum Hall States in Dirac Materials

## TL;DR

This paper explores the optical radiation properties of disordered quantum Hall states in Dirac materials, revealing distinct edge and bulk behaviors that enable new spectroscopic and imaging techniques for quantum Hall edge states and disorder landscapes.

## Contribution

It demonstrates the generation of high multipole moments from edge states and characterizes bulk radiation for imaging disorder, offering novel optical tools for quantum Hall studies.

## Key findings

- Edge radiation exhibits multipole moments > 50, indicating high angular momentum transfer.
- Bulk radiation appears as random dipole emission with disorder-dependent spectral features.
- Optical measurements can image disorder landscapes and probe percolation transitions.

## Abstract

We investigate the optical response of strongly disordered quantum Hall states in two-dimensional Dirac materials and find qualitatively different effects in the radiation properties of the bulk versus the edge. We show that the far-field radiation from the edge is characterized by large multipole moments (> 50) due to the efficient transfer of angular momentum from the electrons into the scattered light. The maximum multipole transition moment is a direct measure of the coherence length of the edge states. Accessing these multipole transitions would provide new tools for optical spectroscopy and control of quantum Hall edge states. On the other hand, the far-field radiation from the bulk appears as random dipole emission with spectral properties that vary with the local disorder potential. We determine the conditions under which this bulk radiation can be used to image the disorder landscape. Such optical measurements can probe sub-micron length scales over large areas and provide complementary information to scanning probe techniques. Spatially resolving this bulk radiation would serve as a novel probe of the percolation transition near half-filling.