Related papers: Zero modes of various graphene configurations from…
One of the most wanted features of holography in its condensed matter physics application is to encode the structure of lattice, which is the most direct data of the material. In this paper, we propose a method to encode the lattice…
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 study zero modes of Laplacians on compact and non-compact metric graphs with general self-adjoint vertex conditions. In the first part of the paper the number of zero modes is expressed in terms of the trace of a unitary matrix…
While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, such a generalized symmetry was so far defined only for a…
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…
Atomic-scale helices exist as motifs for several material lattices. We examine a tight-binding model for a single one-dimensional monatomic chain with a p-orbital basis coiled into a helix. A topologically nontrivial phase emerging from…
\textit{Holey Graphene} (HG) is a widely used graphene material for the synthesis of high-purity and highly crystalline materials. In this work, we explore the electronic properties of a periodic distribution of lattice holes, demonstrating…
Zero energy states in the Dirac spectrum with U(1) symmetric massive vortices of various underlying insulating orders in strained graphene are constructed in the presence of the magnetic field. An easy plane vortex of antiferromagnet and…
We present and discuss in detail practical techniques in formulating effective models to describe the dynamics of low-energy electrons in generic bilayer graphene. Starting from a tight-binding model using the $p_z$ orbital of carbon atoms…
A class of graphene wound into three-dimensional periodic curved surfaces ("graphitic zeolites") is proposed and their electronic structures are obtained to explore how the massless Dirac fermions behave on periodic surfaces. We find in the…
We study the properties of graphene wormholes in which a short nanotube acts as a bridge between two graphene sheets, where the honeycomb carbon lattice is curved from the presence of 12 heptagonal defects. By taking the nanotube bridge…
We have developed an unifying tight-binding Hamiltonian that can account for the electronic properties of recently proposed Si-based nanostructures, namely, Si graphene-like sheets and Si nanotubes. We considered the $sp^3s^*$ and $sp^{3}$…
Dirac-like Hamiltonians, linear in momentum $k$, describe the low-energy physics of a large set of novel materials, including graphene, topological insulators, and Weyl fermions. We show here that the inclusion of a minimal $k^2$ Wilson's…
A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A ``loop'' in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological…
One-dimensional systems with topological order are intimately related to the appearance of zero-energy modes localized on their boundaries. The most common example is the Kitaev chain, which displays Majorana zero-energy modes and it is…
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…
We demonstrate that free graphene sheet edges can curl back on themselves,reconstructing as nanotubes. This results in lower formation energies than any other non-functionalised edge structure reported to date in the literature. We…
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…
We analyze the zero-energy sector of the trigonal zigzag nanodisk and corner based on the Dirac theory of graphene. The zero-energy states are shown to be indexed by the edge momentum and grouped according to the irreducible representation…
The present article discusses magnetic confinement of the Dirac excitations in graphene in presence of inhomogeneous magnetic fields. In the first case a magnetic field directed along the z axis whose magnitude is proportional to $1/r$ is…