Ising instability of a Holstein phonon mode in graphene

TL;DR

This paper investigates a phase transition in graphene's phonon modes caused by electron-phonon interactions, predicting an Ising transition that affects observable properties like Raman scattering.

Contribution

It introduces the concept of an Ising transition in graphene's phonon modes and calculates critical parameters and effects on physical properties.

Findings

Identification of an Ising transition in graphene phonons

Calculation of critical point and phonon frequency renormalization

Predictions for observable effects in Raman scattering and transport

Abstract

We study the thermal distribution of phonons in a graphene sheet. Due to the two electronic bands there are two out-of-plane phonon modes with respect to the two sublattices. One of these modes undergoes an Ising transition by spontaneously breaking the sublattice symmetry. We calculate the critical point, the renormalization of the phonon frequency and the average lattice distortion. This transition might be observable in Raman scattering and in transport properties.