Related papers: An Index Theorem for Graphene

We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported and symmetric, we show that the S-matrix for all energies in any given open set…

We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical…

The electronic structure, specific heat, and thermal conductivity of silicon embedded in a monolayer graphene nanosheet are studied using Density Functional Theory. Two different shapes of the substitutional Si doping in the graphene are…

We show by means of ab initio calculations and tight-binding modeling that an oxide system based on a honeycomb lattice can sustain topologically non-trivial states if a single orbital dominates the spectrum close to the Fermi level. In…

The correlation of odd electrons in graphene turns out to be significant so that the species should be attributed to correlated ones. This finding profoundly influences the computational strategy addressing it to multireference…

Graphene is a quantum spin Hall insulator with a 45 $\mu$eV wide non-trivial topological gap induced by the intrinsic spin-orbit coupling. Even though this zero-field spin splitting is weak, it makes graphene an attractive candidate for…

We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…

We analytically calculate the energy spectrum of a circular graphene quantum dot with radius R subjected to a perpendicular magnetic field B by applying the infinite-mass boundary condition. We can retrieve well-known limits for the cases…

We study the effects of insulating oxides in their crystalline forms on the energy band structure of monolayer and bilayer graphene using a \textit{first principles} density functional theory based electronic structure method and a local…

We obtain analytic expressions for the conductivity of pristine (pure) graphene in the framework of the Dirac model using the polarization tensor in (2+1)-dimensions defined along the real frequency axis. It is found that at both zero and…

We present a simple criterion for solvability of lattice spin systems on the basis of the graph theory and the simplicial homology. The lattice systems satisfy algebras with graphical representations. It is shown that the null spaces of…

In this thesis, we analyze the stochastic completeness of a heat kernel on graphs which is a function of three variables: a pair of vertices and a continuous time, for infinite, locally finite, connected graphs. For general graphs, a…

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,…

We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported, we show that the S-matrix for all energies in any open set in the continuous…

The reflectivity properties of graphene with nonzero mass-gap parameter are investigated in the framework of Dirac model using the polarization tensor in (2+1)-dimensional space-time. For this purpose, a more simple explicit representation…

We present a theory of optimal topological textures in nonlinear sigma-models with degrees of freedom living in the Grassmannian $\mathrm{Gr}(M,N)$ manifold. These textures describe skyrmion lattices of $N$-component fermions in a…

The dispersion relations of carbon nanotubes are often obtained cross-sectioning those of graphene (zone-folding technique) in a rectangular region of the reciprocal space, where it is easier to fold the resulting relations into the…

This is a short non-technical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later…

Electronic states confined to zero angle grain boundaries in single layer graphene are analyzed using topological band theoretic arguments. We identify a hidden chiral symmetry which supports symmetry protected zero modes in projected bulk…

We show that a generalized Dirac structure survives beyond the linear regime of the low-energy dispersion relations of graphene. A generalized uncertainty principle of the kind compatible with specific quantum gravity scenarios with a…