# Thermal Transport Signatures of Broken-Symmetry Phases in Graphene

## TL;DR

This paper predicts how thermal transport measurements can reveal broken-symmetry phases in bilayer graphene's quantum Hall state by analyzing spin and valley wave spectra and the role of Goldstone modes in heat conduction.

## Contribution

It introduces a method to detect spontaneous symmetry breaking in bilayer graphene via thermal transport signatures and analyzes the spectrum of collective excitations in this context.

## Key findings

- Goldstone modes enable heat transport at low temperatures.
- External fields can identify the type of symmetry breaking.
- Temperature dependence reveals gapped mode information.

## Abstract

In the half-filled zero-energy Landau level of bilayer graphene, competing phases with spontaneously broken symmetries and an intriguing quantum critical behavior have been predicted. Here we investigate signatures of these broken-symmetry phases in thermal transport measurements. To this end we calculate the spectrum of spin and valley waves in the $\nu=0$ quantum Hall state of bilayer graphene. The presence of Goldstone modes enables heat transport even at low temperatures, which can serve as compelling evidence for spontaneous symmetry breaking. By varying external electric and magnetic fields it is possible to determine the nature of the symmetry breaking and temperature-dependent measurements may yield additional information about gapped modes.