Electron-induced rippling in graphene

TL;DR

This paper explores how electron-hole interactions influence rippling in graphene, revealing a quantum critical point where ripples emerge from spontaneous symmetry breaking akin to Higgs condensation.

Contribution

It introduces a novel mechanism linking electron-hole excitations to rippling, highlighting a quantum critical point affecting graphene's membrane rigidity.

Findings

Electron-hole exchange interactions can induce a quantum critical point in graphene.

Ripples result from spontaneous symmetry breaking similar to Higgs field condensation.

Membrane tension influences ripple formation, leading to a buckling transition.

Abstract

We show that the interaction between flexural phonons, when corrected by the exchange of electron-hole excitations, may place the graphene sheet very close to a quantum critical point characterized by the strong suppression of the bending rigidity of the membrane. Ripples arise then due to spontaneous symmetry breaking, following a mechanism similar to that responsible for the condensation of the Higgs field in relativistic field theories. In the presence of membrane tensions, ripple condensation may be reinforced or suppressed depending on the sign of the tension, following a zero-temperature buckling transition in which the order parameter is given essentially by the square of the gradient of the flexural phonon field.