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To solve the Dirac equation with the finite difference method, one has to face up to the spurious-state problem due to the fermion doubling problem when using the conventional central difference formula to calculate the first-order…
A key objective of computational solid state physics is to predict electronic properties of periodic materials. However, electronic structure simulations based on density functional theory fail to predict experimental results if…
We study atoms trapped with a harmonic confinement in an optical lattice characterized by a flat band and Dirac cones. We show that such an optical lattice can be constructed which can be accurately described with the tight binding or…
We provide an updated study of some electronic properties of graphene nanoscrolls, exploiting a related curved space Dirac equation for the charge carriers. To this end, we consider an explicit parametrization in cylindrical coordinates,…
The unique linear and massless band structure of graphene, in a purely two-dimensional Dirac fermionic structure, have led to intense research spanning from condensed matter physics to nanoscale device applications covering the electrical,…
In this paper, we analytically investigate the electronic structure of Bernal stacking (AB stacking) graphene evolving from monolayer (a zero-gap semiconductor with a linear Dirac-like spectrum around the Fermi energy) to multi-layer…
Antiferromagnetism in stacked nanographite is investigated with using the Hubbard-type model. We find that the open shell electronic structure can be an origin of the decreasing magnetic moment with the decrease of the inter-graphene…
We analyze the scattering sector of the Hamiltonians for both gapless and gapped graphene in the presence of a charge impurity using the 2D Dirac equation, which is applicable in the long wavelength limit. We show that for certain range of…
We elaborate that single-layer graphene with periodic vacancies can have a band structure containing nodal lines or nodal loops, opening the possibility of graphene-based electronic or spintronic devices with novel functionalities. The…
We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to…
We show how the two-dimensional Dirac oscillator model can describe some properties of electrons in graphene. This model explains the origin of the left-handed chirality observed for charge carriers in monolayer and bilayer graphene. The…
We study the existence and topological stability of Fermi points in a graphene layer and stacks with many layers. We show that the discrete symmetries (spacetime inversion) stabilize the Fermi points in monolayer, bilayer and multilayer…
The electronic properties of hydrogenated graphenes are investigated with the first-principles calculations. Geometric structures, energy bands, charge distributions, and density of states (DOS) strongly depend on the different…
Motivated by recent graphene transport experiments, we have undertaken a numerical study of the conductivity of disordered two-dimensional massless Dirac fermions. Our results reveal distinct differences between the cases of short-range and…
The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first order generalized Dirac equation in the 24-dimensional matrix form. The mass and spin projection…
Man-made artificial graphene has attracted significant attention in the past few years due to the possibilities to construct designer Dirac fermions with unexpected topological properties and applications in nanoelectronics. Here we use a…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
We show that, by going beyond the low-energy approximation for which the dispersion relations of graphene are linear, the corresponding emergent field theory is a specific generalization a Dirac field theory. The generalized Dirac…
We study 1-loop effects for massless Dirac fields in two spatial dimensions, coupled to homogeneous electromagnetic backgrounds, both at zero and at finite temperature and density. In the case of a purely magnetic field, we analyze the…
The propagation of charge carriers in graphene is compared to that in type II/III heterostructures for which a two-band Kane model is appropriate. In particular, conditions for a quantitative analogy between these two cases are searched…