# Cooling of chiral heat transport in the quantum Hall effect graphene

## TL;DR

This paper investigates how hot electrons in graphene under quantum Hall conditions cool down via acoustic phonons, explaining the short cooling length observed experimentally.

## Contribution

It introduces a detailed model of electron-phonon cooling in graphene's quantum Hall edge states considering boundary conditions specific to van der Waals heterostructures.

## Key findings

- Phonon emission explains the observed short cooling length.
- Temperature profiles are derived considering boundary conditions.
- Results align with experimental observations.

## Abstract

In the quantum Hall effect (QHE) regime, heat is carried by electrons in the edge states of Landau levels. Here, we study cooling of hot electrons propagating along the edge of graphene at the filling factor $\nu=\pm2$, mediated by acoustic phonons. We determine the temperature profile extended from a hot spot, where the Hall current is injected into graphene from a metallic contact, taking into account specifics of boundary conditions for lattice displacements in graphene in a van der Waals heterostructure with an insulating substrate. Our calculations, performed using generic boundary conditions for Dirac electrons, show that emission of phonons can explain a short cooling length observed in graphene-based QHE devices by Nahm, Hwang and Lee [PRL 110, 226801 (2013)].