Thermal buckling transition of crystalline membranes in a field

TL;DR

This paper investigates the thermal buckling transition of crystalline membranes, like graphene, in a field, revealing a new universality class with modified elasticity exponents and discussing the nature of the transition.

Contribution

It introduces a detailed analysis of the buckling transition in membranes lacking rotational invariance, identifying a new universality class and contrasting theoretical predictions.

Findings

Transition is in a new universality class

Self-consistent screening predicts second order transition

RG suggests a weakly first order transition

Abstract

Two dimensional crystalline membranes in isotropic embedding space exhibit a flat phase with anomalous elasticity, relevant e.g., for graphene. Here we study their thermal fluctuations in the absence of exact rotational invariance in the embedding space. An example is provided by a membrane in an orientational field, tuned to a critical buckling point by application of in-plane stresses. Through a detailed analysis, we show that the transition is in a new universality class. The self-consistent screening method predicts a second order transition, with modified anomalous elasticity exponents at criticality, while the RG suggests a weakly first order transition.