  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 in the
membrane properties. Quantum nuclear effects turn out to be appreciable in
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.
