Related papers: Smooth electron waveguides in graphene
The statistical properties of the carrier density profile of graphene in the ground state in the presence particle-particle interaction and random charged impurity in zero gate voltage has been recently obtained by Najafi \textit{et al.}…
Many of graphene's unique electronic properties emerge from its Dirac-like electronic energy spectrum. Similarly, it is expected that a nanophotonic system featuring Dirac dispersion will open a path to a number of important research…
We present exact analytical zero-energy solutions for a class of smooth decaying potentials, showing that the full confinement of charge carriers in electrostatic potentials in graphene quantum dots and rings is indeed possible without…
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…
It is well-known that the tight-binding Hamiltonian of graphene describes the low-energy excitations that appear to be massless chiral Dirac fermions. Thus, in the continuum limit one can analyze the crystal properties using the formalism…
We develop a suitable technique to design zero-energy graphene models with radial electrostatic potentials capable of achieving electrostatic confinement. Using the Gaussian law for electrostatics, we derive the charge density associated…
It is well-known that macroscopically-normalizable zero-energy wavefunctions of spin-$\frac{1}{2}$ particles in a two-dimensional inhomogeneous magnetic field are spin-polarized and exactly calculable with degeneracy equaling the number of…
We investigate the effect of a periodic potential on the electronic states and conductance of graphene. It is demonstrated that for a cosine potential $V(x)=V_0\cos(G_0x)$, new zero energy states emerge whenever $J_0(\frac {2V_0}{\hbar v_F…
It is highly desirable to modify and improve the Dirac electron system of graphene for novel electronic properties and promising applications. For this purpose, we study 2D heterostructures consisting of graphene and monolayer TMDs by means…
Gauge-theory approach to describe Dirac fermions on a disclinated flexible membrane beyond the inextensional limit is formulated. The elastic membrane is considered as an embedding of 2D surface into R^3. The disclination is incorporated…
At low energy, electrons in doped graphene sheets behave like massless Dirac fermions with a Fermi velocity which does not depend on carrier density. Here we show that modulating a two-dimensional electron gas with a long-wavelength…
We study the confinement of Dirac fermions in armchair graphene nanoribbons by means of a quantum-dot-type electrostatic potential. With the use of specific projection operators, we find exact solutions for some bound states that satisfy…
Confining Dirac fermions in graphene by electrostatic fields is a challenging task. Electric quantum dots created by a scanning tunneling microscope (STM) tip can trap zero-energy quasi-particles. The Lorentzian quantum well provides a…
We provide detailed calculation of the a.c. conductivity in the case of 1/r-Coulomb interacting massless Dirac particles in graphene in the collisionless limit when \omega >> T. The analysis of the electron self-energy, current vertex…
We present extensive numerical results for the thermodynamic density of states (i.e. quantum capacitance) of a two-dimensional massless Dirac fermion fluid in a doped graphene sheet. In particular, by employing the random phase…
Two-dimensional electrons in graphene are known to behave as massless fermions with Dirac-Weyl type linear dispersion near the Dirac crossing points. We have investigated the collective excitations of this system in the presence or absence…
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…
Due to Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design…
It was recently proposed that the interface between a graphene nanoribbon in the canted antiferromagnetic quantum Hall state and a s-wave superconductor may present topological superconductivity, resulting in the appearance of Majorana zero…
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…