Quantum effects in a free-standing graphene lattice: Path-integral against classical Monte Carlo simulations

Abstract

In order to study quantum effects in a two-dimensional crystal lattice of a free-standing monolayer graphene, we have performed both path-integral Monte Carlo (PIMC) and classical Monte Carlo (MC) simulations for temperatures up to 2000 K. The REBO potential is used for the interatomic interaction. The total energy, interatomic distance, root-mean-square displacement of the atom vibrations, and the free energy of the graphene layer are calculated. The obtained lattice vibrational energy per atom from the classical MC simulation is very close to the energy of a three-dimensional harmonic oscillator 3k B T . The PIMC simulation shows that quantum effects due to zero-point vibrations are significant for temperatures T < 1000 K. The quantum contribution to the lattice vibrational energy becomes larger than that of the classical lattice for T < 400 K. The lattice expansion due to the zero-point motion causes an increase of 0.53% in the lattice parameter. A minimum in the lattice parameter appears at T 500 K. Quantum effects on the atomic vibration amplitude of the graphene lattice and its free energy are investigated.

Quantum effects in graphene monolayers: Path-integral simulations

“…These results are similar to those found in earlier classical Monte Carlo and MD simulations of graphene single In-plane surface (Å layers. 35,39,53 There are two competing effects which explain this temperature dependence of A , as discussed below.…”

“…In any case, one can use A as a helpful variable to carry out simulations of layered systems such as graphene, and indeed it is A which defines the area of the simulation cell in the (x, y) plane. This in-plane area has been studied earlier in several works 31,35,39,53,75 as a function of temperature and external stress, but one can argue that it is not necessarily a variable to which one can associate properties of a real material surface. This can be further illustrated by considering a "real" surface A (in 3D space) for graphene, as can be defined from the actual bonds between carbon atoms.…”

“…This allows to carry out quantitative studies of anharmonic effects in condensed matter. 33,34 Recently, Brito et al 35 have carried out path-integral Monte Carlo simulations of a single graphene layer. These authors examined several equilibrium properties of graphene at finite temperatures using a supercell including 200 carbon atoms.…”

Anharmonic Quantum Effects in Cubic Boron Nitride Crystal by Path Integral Monte Carlo Simulations

“…From the theoretical point of view, there have been several studies showing that anharmonic quantum effects play an important role on the structural and thermodynamic properties of covalent solids, particularly on the quantities such as vibrational energy, volume, mean square displacement, and kinetic energy . When comparisons between quantum and classical systems are possible, the calculated quantities have shown considerable differences, even at the room temperature.…”

“…The PIMC method overcomes the deficiencies of earlier studies since the quantum character of the particles at finite temperature is naturally included. This method has been considered to be one of the most powerful methods to simulate a quantum system at finite temperature with essential contributions to understand the thermodynamic properties of several different systems, mainly in the condensed matter . Nevertheless, in order to make quantitative estimates of the quantum effects in c‐BN crystal as a function of applied temperature and pressure, we compare the calculation results from the PIMC simulations with those from the classical Monte Carlo.…”