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.
We study the effect of atomic relaxation on the structure of moire patterns in twisted graphene on graphite and double layer graphene by large scale atomistic simulations. The reconstructed structure can be described as a superlattice of `hot spots w
ith vortex-like behaviour of in-plane atomic displacements and increasing out-of-plane displacements with decreasing angle. These lattice distortions affect both scalar and vector potential and the resulting electronic properties. At low misorientation angles (<$sim$1$^circ$) the optimized structures deviate drastically from the sinusoidal modulation which is often assumed in calculations of the electronic properties. The proposed structure might be verified by scanning probe microscopy measurements.
By atomistic modeling of moir{e} patterns of graphene on a substrate with a small lattice mismatch, we find qualitatively different strain distributions for small and large misorientation angles, corresponding to the commensurate-incommensurate trans
ition recently observed in graphene on hexagonal BN. We find that the ratio of C-N and C-B interactions is the main parameter determining the different bond lengths in the center and edges of the moir{e} pattern. Agreement with experimental data is obtained only by assuming that the C-B interactions are at least twice weaker than the C-N interactions. The correspondence between the strain distribution in the nanoscale moir{e} pattern and the potential energy surface at the atomic scale found in our calculations, makes the moir{e} pattern a tool to study details of dispersive forces in van der Waals heterostructures.
Imperfections in the crystal structure, such as point defects, can strongly modify the optical and transport properties of materials. Here, we study the effect of point defects on the optical and DC conductivities of single layers of semiconducting t
ransition metal dichalcogenides with the form $M$S$_2$, where $M$=Mo or W. The electronic structure is considered within a six bands tight-binding model, which accounts for the relevant combination of $d$ orbitals of the metal $M$ and $p$ orbitals of the chalcogen $S$. We use the Kubo formula for the calculation of the conductivity in samples with different distributions of disorder. We find that $M$ and/or S defects create mid-gap states that localize charge carriers around the defects and which modify the optical and transport properties of the material, in agreement with recent experiments. Furthermore, our results indicate a much higher mobility for $p$-doped WS$_2$ in comparison to MoS$_2$.
Motivated by the observation of ferromagnetism in carbon foams, a massive search for (meta)stable disorder structures of elemental carbon is performed by a generate and test approach. We use the Density Functional based program SIESTA to optimize the
structures and calculate the electronic spectra and spin densities. About 1% of the 24000 optimized structures presents magnetic moments, a necessary but not sufficient condition for intrinsic magnetic order. We analyze the results using elements of graph theory. Although the relation between structure and the occurrence of magnetic moments is not yet fully clarified, we give some minimal requirements for this possibility, such as the existence of three-fold coordinated atoms surrounded by four-fold coordinated atoms. We discuss in detail the most promising structures.
The low energy effective field model for the multilayer graphene (at ABC stacking) is considered. We calculate the effective action in the presence of constant external magnetic field $B$ (normal to the graphene sheet). We also calculate the first tw
o corrections to this effective action caused by the in-plane electric field $E$ at $E/B ll 1$ and discuss the magnetoelectric effect. In addition, we calculate the imaginary part of the effective action in the presence of constant electric field $E$ and the lowest order correction to it due to the magnetic field ($B/E ll 1$).
In this work, we investigate the adsorption of a single cobalt atom (Co) on graphene by means of the complete active space self-consistent field approach, additionally corrected by the second-order perturbation theory. The local structure of graphene
is modeled by a planar hydrocarbon cluster (C$_{24}$H$_{12}$). Systematic treatment of the electron correlations and the possibility to study excited states allow us to reproduce the potential energy curves for different electronic configurations of Co. We find that upon approaching the surface, the ground-state configuration of Co undergoes several transitions, giving rise to two stable states. The first corresponds to the physisorption of the adatom in the high-spin $3d^74s^2$ ($S=3/2$) configuration, while the second results from the chemical bonding formed by strong orbital hybridization, leading to the low-spin $3d^9$ ($S=1/2$) state. Due to the instability of the $3d^9$ configuration, the adsorption energy of Co is small in both cases and does not exceed 0.35 eV. We analyze the obtained results in terms of a simple model Hamiltonian that involves Coulomb repulsion ($U$) and exchange coupling ($J$) parameters for the 3$d$ shell of Co, which we estimate from first-principles calculations. We show that while the exchange interaction remains constant upon adsorption ($simeq1.1$ eV), the Coulomb repulsion significantly reduces for decreasing distances (from 5.3 to 2.6$pm$0.2 eV). The screening of $U$ favors higher occupations of the 3$d$ shell and thus is largely responsible for the interconfigurational transitions of Co. Finally, we discuss the limitations of the approaches that are based on density functional theory with respect to transition metal atoms on graphene, and we conclude that a proper account of the electron correlations is crucial for the description of adsorption in such systems.
We compute, in topological terms, the spectral flow of an arbitrary family of self-adjoint Dirac type operators with classical (local) boundary conditions on a compact Riemannian manifold with boundary under the assumption that the initial and termin
al operators of the family are conjugate by a bundle automorphism. This result is used to study conditions for the existence of nonzero spectral flow of a family of self-adjoint Dirac type operators with local boundary conditions in a two-dimensional domain with nontrivial topology. Possible physical realizations of nonzero spectral flow are discussed.
We discuss quantum electrodynamics emerging in the vacua with anisotropic scaling. Systems with anisotropic scaling were suggested by Horava in relation to the quantum theory of gravity. In such vacua the space and time are not equivalent, and moreov
er they obey different scaling laws, called the anisotropic scaling. Such anisotropic scaling takes place for fermions in bilayer graphene, where if one neglects the trigonal warping effects the massless Dirac fermions have quadratic dispersion. This results in the anisotropic quantum electrodynamics, in which electric and magnetic fields obey different scaling laws. Here we discuss the Heisenberg-Euler action and Schwinger pair production in such anisotropic QED
Self consistent renormalization theory of itinerant ferromagnets is used to calculate the Curie temperature of clusters down to approximately 100 atoms in size. In these clusters the electrons responsible for the magnetic properties are assumed to be
(weakly) itinerant. It is shown that the Curie temperature can be larger than in the bulk. The effect originates from the phenomenon of level repulsion in chaotic quantum systems, which suppresses spin fluctuations. Since the latter destroy the magnetic order the resulting Curie temperature increases, contrary to expectations of the naive Stoner picture. The calculations are done assuming that the energy levels of the cluster are described by the Gaussian Orthogonal Ensemble of random matrix theory.
