Buckling of thermalized sheets

Two dimensional atomically thin membranes (ATMs), such as graphene and transition metal dichalcogenides, display exceptional properties that have been exploited in advanced electronic applications. In this talk, we utilize tools from statistical physics and molecular dynamics simulations to investigate how thermal fluctuation affect buckling of ATMs. Of special interest are ATMs that are larger than the characteristic thermal length scale lth, which is a function of temperature and material constants. Both simulations and theory predict that for small sheets of size L<<lth the critical buckling load coincides with the classical continuum theory σ ~ L^(-2). However, for large sheets of size L>>lth thermal fluctuations effectively stiffen the bending rigidity, which increases the critical buckling load that scales as σ ~ L^(-2+η). Here η~0.8 is the universal exponent that is related to the increased bending rigidity. We demonstrate that the critical buckling load scales the same way for both periodic and clamped boundary conditions. These results shed light on fundamental mechanisms that underlie buckling of ATMs and make possible accurate predictions that can be used for design purposes in applications.