Related papers: Topological effects, index theorem and supersymmet…
Physics of topological materials have attracted much attention from both physicists and mathematicians recently. The index and the fermion number of Dirac fermions play an important role in topological insulators and topological…
Proximity orbital and spin-orbital effects of graphene on monolayer transition-metal dichalcogenides (TMDCs) are investigated from first-principles. The Dirac band structure of graphene is found to lie within the semiconducting gap of TMDCs…
We point out that the zero-energy Landau level of Dirac fermions in graphene can be, in the presence of a repulsive electron-electron interaction, split into two (levels) associated with a "bond ordering" formation having a "Kekule…
Graphene and topological insulators (TI) possess two-dimensional Dirac fermions with distinct physical properties. Integrating these two Dirac materials in a single device creates interesting opportunities for exploring new physics of…
Inspired by a recent discovery of a peculiar integer quantum Hall effect (QHE) in graphene, we study QHE on a honeycomb lattice in terms of the topological quantum number, with two-fold interests: First, how the zero-mass Dirac QHE around…
Motivated by recent results on the index of the Dirac operator D={\gamma}^{{\mu}}D_{{\mu}} of QCD on lattice and also by results on topological features of electrons and holes of 2-dimensional graphene, we compute in this paper the Index of…
The spurious states found in numerical implementations of envelope function models for semiconductor heterostructures and nanostructures have been shown to be readily removed by employing a first-order difference scheme. This approach is…
We unveil novel spin-orbit torque mechanisms driven by topological edge states in magnetic graphene-based devices. Within the energy gap, a damping-like torque plateau emerges within the quantum anomalous Hall phase upon breaking…
In this paper, we study the massive Dirac equation with the presence of the Morse potential in polar coordinate. The Dirac Hamiltonian is written as two second-order differential equations in terms of two spinor wavefunctions. Since the…
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…
Systematic tight-binding investigations of the electronic spectra (as a function of the magnetic field) are presented for trigonal graphene nanoflakes with reconstructed zigzag edges, where a succession of pentagons and heptagons, that is…
Effective topological field theories describe the properties of Dirac fermions in the low-energy regime. In this work, we introduce a new emergent gravity model by considering Dirac fermions invariant under local de Sitter transformations…
We study the graphene lattice with a curvature effect. The action depicting multilayers of graphene is portrayed in curved spacetime and effective Dirac equation scopes the curvature effect. The magnetic field is responsible for the…
A generalized algebra of noncommutative coordinates and momenta embracing non-Abelian gauge fields is proposed. Through a two-dimensional realization of this algebra for a gauge field including electromagnetic vector potential and two…
We study uniaxially strained graphene under the influence of non-uniform magnetic fields perpendicular to the material sample with a coordinate independent strain tensor. For that purpose, we solve the Dirac equation with anisotropic Fermi…
This review aims at a theoretical discussion of Dirac points in two-dimensional systems. Whereas Dirac points and Dirac fermions are prominent low-energy electrons in graphene (two-dimensional graphite), research on Dirac fermions in…
We analyze a gap equation for the propagator of Dirac quasiparticles and conclude that in graphene in a magnetic field, the order parameters connected with the quantum Hall ferromagnetism dynamics and those connected with the magnetic…
Among many remarkable qualities of graphene, its electronic properties attract particular interest due to a massless chiral character of charge carriers, which leads to such unusual phenomena as metallic conductivity in the limit of no…
We derive an index theorem for the Dirac operator in the background of various topological excitations on an R^3 \times S^1 geometry. The index theorem provides more refined data than the APS index for an instanton on R^4 and reproduces it…
The families index theory for the overlap lattice Dirac operator is applied to derive topological features of the space of SU(N) lattice gauge fields on the 4-torus: The topological sectors, specified by the fermionic topological charge,…