Thermal properties of graphene from path-integral simulations

Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres

Path integral Monte Carlo and closure computations are utilized to study real space triplet correlations in the quantum hard-sphere system. The conditions cover from the normal fluid phase to the solid phases face-centered cubic (FCC) and cI16 (de Broglie wavelengths , densities ). The focus is on the equilateral and isosceles features of the path-integral centroid and instantaneous structures. Complementary calculations of the associated pair structures are also carried out to strengthen structural identifications and facilitate closure evaluations. The three closures employed are Kirkwood superposition, Jackson-Feenberg convolution, and their average (AV3). A large quantity of new data are reported, and conclusions are drawn regarding (i) the remarkable performance of AV3 for the centroid and instantaneous correlations, (ii) the correspondences between the fluid and FCC salient features on the coexistence line, and (iii) the most conspicuous differences between FCC and cI16 at the pair and the triplet levels at moderately high densities (. This research is expected to provide low-temperature insights useful for the future related studies of properties of real systems (e.g., helium, alkali metals, and general colloidal systems).

Heat capacity in doped graphene under magnetic fields: the role of spin splitting

We study the electronic heat capacity in doped graphene under magnetic fields. The partition function is calculated considering only the thermal excitations in the last occupied energy levels. Due to the large energy separation between the Landau levels (LLs) and the Zeeman splitting, at low temperatures the heat capacity is dominated by the spin excitations in the last occupied LL. Correspondingly the heat capacity oscillates with maximum amplitude at half filling of each LL. At higher temperatures the inter-LLs excitations dominate the heat capacity, with maximum amplitude at full filling factors. The oscillation amplitudes are compared with the phonon heat capacityCp. It is shown that the spin induced heat capacity oscillations have a maximum amplitude approaching 3% ofCp, whereas for the inter-LLs excitations the maximum amplitude is only 0.1% ofCp. These amplitudes decrease in the presence of impurities, although the effect is appreciable if the LLs broadening is bigger than the excitation energies.

Phonon dispersion in two-dimensional solids from atomic probability distributions

We propose a harmonic linear response (HLR) method to calculate the phonon dispersion relations of two-dimensional layers from equilibrium simulations at finite temperatures. This HLR approach is based on the linear response of the system, as derived from the analysis of its centroid density in equilibrium path integral simulations. In the classical limit, this approach is closely related to those methods that study vibrational properties by the diagonalization of the covariance matrix of atomic fluctuations. The validity of the method is tested in the calculation of the phonon dispersion relations of a graphene monolayer, a graphene bilayer, and graphane. Anharmonic effects in the phonon dispersion relations of graphene are demonstrated by the calculation of the temperature dependence of the following observables: the kinetic energy of the carbon atoms, the vibrational frequency of the optical E_2g mode, and the elastic moduli of the layer.

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 T _m that permits us to calculate T _m. The results obtained lay a theoretical foundation for an analog of Lindemann criterion for graphene.