相关论文: Zero Energy States for a Class of Two-Dimensional …
We devise a supersymmetry-based method for the construction of zero-energy states in graphene. Our method is applied to a two-dimensional massless Dirac equation with a hyperbolic scalar potential. We determine supersymmetric partners 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 known that the excitations in graphene-like materials in external electromagnetic field are described by solutions of massless two-dimensional Dirac equation which includes both Hermitian off-diagonal matrix and scalar potentials. Up…
The low energy excitations of graphene can be described by a massless Dirac equation in two spacial dimensions. Curved graphene is proposed to be described by coupling the Dirac equation to the corresponding curved space. This covariant…
Using the concept of complex non PT symmetric potential we study creation of zero energy states in graphene by a scalar potential. The admissible range of the potential parameter values for which such states exist has been examined. The…
The complete theory of electrical conductivity of graphene at arbitrary temperature is developed with taken into account mass-gap parameter and chemical potential. Both the in-plane and out-of-plane conductivities of graphene are expressed…
The Dirac equation with a U(1) vortex in the mass-term is solved in the presence of magnetic-like fields at zero energy. By drawing an analogy to classical mechanics, it is shown that the four-component Dirac equation in arbitrary magnetic…
We present exact analytical solutions for the zero-energy modes of two-dimensional massless Dirac fermions fully confined within a smooth one-dimensional potential V(x)= - {\alpha}/cosh({\beta}x), which provides a good fit for potential…
In the present paper, a systematic approach is presented for solution of two-dimensional massless Dirac equation with external electrostatic potential applied. This approach is based on the new - asymmetric - form of SUSY-like intertwining…
We utilize the relation between soliton solutions of the mKdV and the combined mKdV-KdV equation and the Dirac equation to construct electrostatic fields which yield exact zero energy states of graphene.
The intertwining relations between superpartner Hamiltonians are the main ingredients of well known Supersymmetrical Quantum Mechanics (SUSY QM). In the present paper, the generalized form of intertwining is used for investigation of a…
We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies, and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac…
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…
Solutions of the one dimensional Dirac equation with piece-wise constant potentials are presented using standard methods. These solutions show that the Klein Paradox is non-existent and represents a failure to correctly match solutions…
We study the two-dimensional massless Dirac equation for a potential that is allowed to depend on the energy and on one of the spatial variables. After determining a modified orthogonality relation and norm for such systems, we present an…
We consider Dirac equation in $(2+1)$ dimensional curved spacetime in the presence of a scalar potential. It is then shown that the zero energy states are degenerate and they can be obtained when the momentum $k_y$ in the $y$ direction…
This work was firstly published in 1986 \cite{we}. No real two-dimensional object with the zero-gap quasi-relativistic spectrum was known in that time. Such an object is well known now: this is graphene. That is why we decided to present it…
The study of vacancies in graphene is a topic of growing interest. A single vacancy induces a localized stable charge of order unity interacting with other charges of the conductor through an unscreened Coulomb potential. It also breaks the…
We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that,…
We study the energy levels of graphene magnetic circular quantum dot surrounded by an infinite graphene sheet in the presence of an electrostatic potential. We solve Dirac equation to derive the solutions of energy spectrum associated with…