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We present an approach to the melting of graphene based on nucleation theory for a first order phase transition from the 2D solid to the 3D liquid via an intermediate quasi-2D liquid. The applicability of nucleation theory, supported by the results of systematic atomistic Monte Carlo simulations, provides an intrinsic definition of the melting temperature of graphene, $ T_m $, and allows us to determine it. We find $T_m simeq 4510$ K, about 250 K higher than that of graphite using the same interatomic interaction model. The found melting temperature is shown to be in good agreement with the asymptotic results of melting simulations for finite disks and ribbons of graphene. Our results strongly suggest that graphene is the most refractory of all known materials.
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The phonon thermal contribution to the melting temperature of nano-particles is inspected. Unlike in periodic boundary condition, under a general boundary condition the integration volume of low energy phonon for a nano-particle is more complex. We estimate the size-dependent melting temperature through the phase shift of the low energy phonon mode acquired by its scattering on boundary surface. A nano-particle can have either a rising or a decreasing melting temperature due to the boundary condition effect, and we found that an upper melting temperature bound exists for a nano-particle in various environments. Moreover, the melting temperature under a fixed boundary condition sets this upper bound.
Assuming diffusive carrier transport and employing an effective medium theory, we calculate the temperature dependence of bilayer graphene conductivity due to Fermi-surface broadening as a function of carrier density. We find that the temperature dependence of the conductivity depends strongly on the amount of disorder. In the regime relevant to most experiments, the conductivity is a function of T/T*, where T* is the characteristic temperature set by disorder. We demonstrate that experimental data taken from various groups collapse onto a theoretically predicted scaling function.
In our publication from 8 years ago (Phys. Rev. B {bf 84}, 115119 (2011)) we calculated RKKY interaction between two magnetic impurities adsorbed on graphene at zero temperature. We show in this short paper that the approach based on Matsubara formalism and perturbation theory for the thermodynamic potential in the imaginary time and coordinate representation which was used then, can be easily generalized, and calculate RKKY interaction between the magnetic impurities at finite temperature.
Multilayer graphene (MLG) thin films are deposited on silicon oxide substrates by mechanical exfoliation (or scotch-tape method) from Kish graphite. The thickness and number of layers are determined from both Atomic Force Microscopy (AFM) and Raman Spectroscopy. Electrical terminals are deposited on MLGs in a four-probe configuration by electron-beam lithography, gold/titanium thermal evaporation, and lift-off. The electrical resistance is measured from room temperature down to 2 K. The electrical resistance of the MLGs shows an increase with decreasing temperature, and then decreases after reaching a maximum value. These results are compared with recent experimental and theoretical data from the literature.
Stochastic switching between the two bistable states of a strongly driven mechanical resonator enables detection of weak signals based on probability distributions, in a manner that mimics biological systems. However, conventional silicon resonators at the microscale require a large amount of fluctuation power to achieve a switching rate in the order of a few Hertz. Here, we employ graphene membrane resonators of atomic thickness to achieve a stochastic switching rate of 7.8 kHz, which is 200 times faster than current state-of-the-art. The (effective) temperature of the fluctuations is approximately 400 K, which is 3000 times lower than the state-of-the-art. This shows that these membranes are potentially useful to transduce weak signals in the audible frequency domain. Furthermore, we perform numerical simulations to understand the transition dynamics of the resonator and derive simple analytical expressions to investigate the relevant scaling parameters that allow high-frequency, low-temperature stochastic switching to be achieved in mechanical resonators.
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