Related papers: An Index Theorem for Graphene

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…

In this paper, we propose a novel framework for modeling topological phases of matter using code-based Narain conformal field theories (NCFTs). We show that the algebraic structure of the NCFTs naturally embeds into critical lattice quantum…

Graphene's original promise to succeed silicon faltered due to pervasive edge disorder in lithographically patterned deposited graphene and the lack of a new electronics paradigm. Here we demonstrate that the annealed edges in…

As a particular application of the earlier proposed model of graphene as a macromolecule, we found the exact analytical expression of dispersion relation for the band of edge states in graphene zigzag ribbons. This band is often referred to…

We evaluate the electronic transmission and conductance in bilayer graphene through a finite number of potential barriers. Further, we evaluate the dispersion relation in a bilayer graphene superlattice with a periodic potential applied to…

Carbon allotropes such as diamond, nano-tube, Fullerene, and Graphene, have unique lattice symmetries of crystal lattice, but these are topologically trivial. We have proposed a topologically-nontrivial allotrope, named Hopfene, which has…

The formation of graphen-nanotube composites addresses a few basic problems. First, both partners are good donors and acceptors of electrons, which significantly complicates the intermolecular interaction between them leading to a two-well…

The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of Neuberger's lattice Dirac operator, is shown to have analogous properties…

We demonstrate the electrical control of topological interface modes at the interface between a graphene-based photonic superlattice and a uniform dielectric medium. Specifically, by integrating graphene sheets into the unit cell of…

'Magic'-angle twisted bilayer graphene has received a lot of interest due to its flat bands with potentially non-trivial topology that lead to intricate correlated phases. A spectrum with flat bands, however, does not require a twist…

We present a minimal but crucial microscopic theory for epitaxial graphene and graphene nanoribbons on the 4H-SiC(0001) surface -- protopypical materials to explore physical properties of graphene in large scale. Coarse-grained model…

We calculate the phonon spectrum for a graphene sheet resulting from the model proposed by T. Lenosky et al. (Nature 355, 333 (1992)) for the free energy of the lattice. This model takes into account not only the usual bond bending and…

The role of defect-induced zero-energy modes on charge transport in graphene is investigated using Kubo and Landauer transport calculations. By tuning the density of random distributions of monovacancies either equally populating the two…

The Witten index for certain supersymmetric lattice models treated by de Boer, van Eerten, Fendley, and Schoutens, can be formulated as a topological invariant of simplicial complexes arising as independence complexes of graphs. We prove a…

We study the electronic states of narrow graphene ribbons (``nanoribbons'') with zigzag and armchair edges. The finite width of these systems breaks the spectrum into an infinite set of bands, which we demonstrate can be quantitatively…

Topology and electron interactions are two central themes in modern condensed matter physics. Here we propose graphene based systems where both the band topology and interaction effects can be simply controlled with electric fields. We…

We perform a detailed analysis of electronic polarizability of graphene with different theoretical approaches. From Kubo's linear response formalism, we give a general expression of frequency and wave-vector dependent polarizability within…

The impact of the electron-electron Coulomb interaction on the optical conductivity of graphene has led to a controversy that calls into question the universality of collisionless transport in this and other Dirac materials. Using a lattice…

The low energy physics of both graphene and surface states of three-dimensional topological insulators is described by gapless Dirac fermions with linear dispersion. In this work, we predict the emergence of a "heavy" Dirac fermion in a…

Graphene has attracted enormous interests due to its unique physical, mechanical, and electrical properties. Specially, graphene-based field-effect transistors (FETs) have evolved rapidly and are now considered as an option for conventional…