Graphene thermal break-down induced by anharmonic bending mode

A novel approach is proposed allowing us to prove, self-consistently, that free-standing graphene reaching a certain temperature loses its mechanical stability resulting in abrupt breakdown, which can be interpreted as melting. Our study is based on the idea of the crucial role of the anomalously soft bending 'sound' mode in the jump transition of graphene from the state with relatively small bending fluctuations to a state with fluctuations close in amplitude to the graphene lattice constant. The acme of the developed theory is in establishing a quantitative relationship connecting the graphene elastic moduli of second, third (negative!), and fourth orders at the melting temperature Tm that permits us to calculate Tm. The results obtained lay a theoretical foundation for an analog of Lindemann criterion for graphene.