# Interaction effects in a chaotic graphene quantum billiard

## TL;DR

This study explores the electronic and magnetic properties of a chaotic graphene quantum billiard, revealing superstructures, Umklapp processes, Coulomb interactions, and potential applications in spintronics.

## Contribution

It provides new insights into the interplay of scattering, Coulomb interactions, and magnetic properties in a chaotic graphene quantum billiard.

## Key findings

- Observation of superstructure and overtones in STM measurements.
- Identification of Coulomb interaction effects on density of states.
- Revealed magnetic properties relevant for spintronic applications.

## Abstract

We investigate the local electronic structure of a Sinai-like, quadrilateral graphene quantum billiard with zigzag and armchair edges using scanning tunneling microscopy at room temperature. It is revealed that besides the $(\sqrt{3}\times\sqrt{3})R30${\deg} superstructure, which is caused by the intervalley scattering, its overtones also appear in the STM measurements, which are attributed to the Umklapp processes. We point out that these results can be well understood by taking into account the Coulomb interaction in the quantum billiard, accounting for both the measured density of state values and the experimentally observed topography patterns. The analysis of the level-spacing distribution substantiates the experimental findings as well. We also reveal the magnetic properties of our system which should be relevant in future graphene based electronic and spintronic applications.