Irreversibility in response to forces acting on graphene sheets

TL;DR

This paper investigates the irreversibility of force responses in suspended graphene sheets, revealing how compression-relaxation mechanisms induce static ripples and identifying a critical temperature influencing ripple stability.

Contribution

It introduces the concept of irreversibility in graphene's response to forces and links ripple formation to a temperature-dependent free-energy difference.

Findings

Static ripples are produced by compression-relaxation mechanisms.

A critical temperature T_c determines ripple stability.

T_c increases with sample size.

Abstract

The amount of rippling in graphene sheets is related to the interactions with the substrate or with the suspending structure. Here, we report on an irreversibility in the response to forces that act on suspended graphene sheets. This may explain why one always observes a ripple structure on suspended graphene. We show that a compression-relaxation mechanism produces static ripples on graphene sheets and determine a peculiar temperature $T_c$, such that for $T<T_c$ the free-energy of the rippled graphene is smaller than that of roughened graphene. We also show that $T_c$ depends on the structural parameters and increases with increasing sample size.