Related papers: An Index Theorem for Graphene
We explore the rotational degree of freedom between graphene layers via the simple prototype of the graphene twist bilayer, i.e., two layers rotated by some angle $\theta$. It is shown that, due to the weak interaction between graphene…
We demonstrate that the electronic spectrum of graphene in a one-dimensional periodic potential will develop a Landau level spectrum when the potential magnitude varies slowly in space. The effect is related to extra Dirac points generated…
We study the transport properties of a neutral graphene sheet with curved regions induced or stabilized by topological defects. The proposed model gives rise to Dirac fermions in a random magnetic field and in the random space dependent…
We consider periodic Schr\"{o}dinger operators on the hexagonal lattice with self-adjoint vertex conditions that allow discontinuity and concentrated mass at the vertices. This model generalizes the periodic Schr\"{o}dinger operator on the…
The low energy continuum limit of graphene is effectively known to be modeled using Dirac equation in (2+1) dimensions. We consider the possibility of using modulated high frequency periodic driving of a two-dimension system (optical…
We consider weighted graphs with an infinite set of vertices. We show that boundedness of all functions of finite energy can be seen as a notion of `relative compactness' for such graphs and study sufficient and necessary conditions for…
Flat bands are of significant interest due to their potential for energy confinement and their ability to enable strongly correlated physics. Incorporating topology into flatband systems further enhances flatband mode robustness against…
An application of quantum size carbon structures--graphenes as electrodes of supercapacitors is studied. A fundamental limit of energy and power density arising from quantum nature of objects due to singularity in graphene density of states…
Graphene has been studied in detail due to its mechanical, electrical, and thermal properties. It is well documented that the introduction of dopants or defects in the lattice can be used to tune material properties for a specific…
We study topological properties of classical spherical center vortices with the low-lying eigenmodes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations. In…
Graphene in the presence of a strong external magnetic field is a unique attraction for investigations of the fractional quantum Hall (fQH) states with odd and even denominators of the fraction. Most of the attempts to understand Graphene…
Graphene was the first material predicted to be a time-reversal-invariant topological insulator; however, the insulating gap is immeasurably small owing to the weakness of spin-orbit interactions in graphene. A recent experiment [1]…
A formalism is proposed to study the electronic and transport properties of graphene sheets with corrugations as the one recently synthesized. The formalism is based on coupling the Dirac equation that models the low energy electronic…
We investigate the reflectance of a dielectric plate coated with a graphene sheet which possesses the nonzero energy gap and chemical potential at any temperature. The general formalism for the reflectance using the polarization tensor is…
Color superconductivity in high density QCD exhibits the color-flavor locked (CFL) phase. To explore zero modes in the CFL phase in the presence of a non-Abelian vortex with an SU(2) symmetry in the vortex core, we apply the index theorem…
A theory of the long wavelength low energy electronic structure of graphite-derived nanotubules is presented. The propagating $\pi$ electrons are described by wrapping a massless two dimensional Dirac Hamiltonian onto a curved surface. The…
We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural…
In this paper, we develop a theory of edge effects in graphene for its applications to nanoantennas in the terahertz, infrared, and visible frequency ranges. Its characteristic feature is selfconsistence reached due the formulation in terms…
Allotropes of carbon, including one-dimensional carbon nanotubes and two-dimensional graphene sheets, continue to draw attention as promising platforms for probing the physics of electrons in lower dimensions. Recent research has shown that…
Energetic and geometric aspects of the permeation of low-Z atoms through graphene sheets are investigated. Energy barriers and deformations are calculated via density functional theory for the permeation of H, He, Li and Be atoms at several…