Path-integral simulation of graphene monolayers under tensile stress

Finite-temperature properties of graphene monolayers under tensile stress have been studied by path-integral molecular dynamics (PIMD) simulations. This method allows one to consider the quantization of vibrational modes in these crystalline membranes and to analyze the influence of anharmonic effects on the membrane properties. Quantum nuclear effects turn out to be appreciable on the structural and thermodynamic properties of graphene at low temperature, and they can even be noticeable at room temperature. Such quantum effects become more relevant as the applied stress is increased, mainly for properties related to out-of-plane atomic vibrations. The relevance of quantum dynamics in the out-of-plane motion depends on the system size, and is enhanced by tensile stress. For applied tensile stresses, we analyze the contribution of the elastic energy to the internal energy of graphene. Results of PIMD simulations are compared with calculations based on a harmonic approximation for the vibrational modes of the graphene lattice. This approximation describes rather well the structural properties of graphene, provided that the frequencies of ZA (flexural) acoustic modes in the transverse direction include a pressure-dependent correction.