A glassy phase in quenched disordered graphene and crystalline membranes

TL;DR

This paper reveals a potential low-temperature glassy phase in quenched disordered graphene and crystalline membranes, identified through a nonperturbative renormalization group approach showing a second order phase transition.

Contribution

It introduces a nonperturbative RG analysis of disordered membranes, uncovering a new finite-temperature, finite-disorder fixed point indicating a glassy phase.

Findings

Identification of a second order phase transition controlled by a finite-temperature fixed point.

Existence of a zero-temperature, finite-disorder fixed point separating different phases.

Evidence for a low-temperature glassy phase in disordered graphene and similar materials.

Abstract

We investigate the flat phase of $D$-dimensional crystalline membranes embedded in a $d$-dimensional space and submitted to both metric and curvature quenched disorders using a nonperturbative renormalization group approach. We identify a second order phase transition controlled by a finite-temperature, finite-disorder fixed point unreachable within the leading order of $\epsilon=4-D$ and $1/d$ expansions. This critical point divides the flow diagram into two basins of attraction: that associated to the finite-temperature fixed point controlling the long distance behaviour of disorder-free membranes and that associated to the zero-temperature, finite-disorder fixed point. Our work thus strongly suggests the existence of a whole low-temperature glassy phase for quenched disordered graphene, graphene-like compounds and, more generally, crystalline membranes.