arXiv subjects

Hocine Bahlouli

Publications and source records attributed to Hocine Bahlouli.

52 records · Page 3Linked to original sources

arXiv2016

Transmission through Biased Graphene Strip

We solve the 2D Dirac equation describing graphene in the presence of a linear vector potential. The discretization of the transverse momentum due to the infinite mass boundary condition reduced our 2D Dirac equation to an effective massive 1D Dirac equation with an effective mass equal to the quantized transverse momentum. We use both a numerical Poincare Map approach, based on space discretization of the original Dirac equation, and direct analytical method. These two approaches have been used to study tunneling phenomena through a biased graphene strip. The numerical results generated by the Poincare Map are in complete agreement with the analytical results.

cond-mat.mes-hall↗

arXiv2016

Controllable Goos-Hänchen Shift in Graphene Triangular Double Barrier

We study the Goos-Hänchen shifts for Dirac fermions in graphene scattered by a triangular double barrier potential. The massless Dirac-like equation was used to describe the scattered fermions by such potential configuration. Our results show that the GHL shifts is affected by the geometrical structure of the double barrier. In particular the GHL shifts change sign at the transmission zero energies and exhibit enhanced peaks at each bound state associated with the double barrier when the incident angle is less than the critical angle associated with the total reflection.

cond-mat.mes-hall↗

arXiv2015

Transmission via Triangular Double Barrier and Magnetic Fields in Graphene

We study the transmission probability of Dirac fermions in graphene scattered by a triangular double barrier potential in the presence of an external magnetic field. Our system made of two triangular potential barrier regions separated by a well region characterized by an energy gap $G_p$. Solving our Dirac-like equation and matching the solutions at the boundaries we express our transmission and reflection coefficients in terms of transfer matrix. We show in particular that the transmission exhibits oscillation resonances that are manifestation of the Klein tunneling effect.

cond-mat.mes-hall↗

arXiv2015

Transmission and Goos-Hänchen like Shifts through a Graphene Double Barrier in an Inhomogeneous Magnetic Field

We studied the transport properties of electrons in graphene as they are scattered by a double barrier potential in the presence of an inhomogeneous magnetic field. We computed the transmission coefficient and Goos-Hänchen like shifts for our system and noticed that transmission is not allowed for certain range of energies. In particular, we found that, in contrast to the electrostatic barriers, the magnetic barriers are able to confine Dirac fermions. We also established some correlation between the electronic transmission properties of Dirac fermions with the Goos-Hänchen like shifts, as reflected in the numerical data.

cond-mat.mes-hall↗

arXiv2015

Double Barriers and Magnetic Field in Bilayer Graphene

We study the transmission probability in an AB-stacked bilayer graphene of Dirac fermions scattered by a double barrier structure in the presence of a magnetic field. We take into account the full four bands of the energy spectrum and use the boundary conditions to determine the transmission probability. Our numerical results show that for energies higher than the interlayer coupling, four ways for transmission probabilities are possible while for energies less than the height of the barrier, Dirac fermions exhibits transmission resonances and only one transmission channel is available. We show that, for AB-stacked bilayer graphene, there is no Klein tunneling at normal incident. We find that the transmission displays sharp peaks inside the transmission gap around the Dirac point within the barrier regions while they are absent around the Dirac point in the well region. The effect of the magnetic field, interlayer electrostatic potential and various barrier geometry parameters on the transmission probabilities are also discussed.

cond-mat.mes-hall↗

arXiv2015

Transmissions in Graphene through Double Barriers and Periodic Potential

Transmission of Dirac fermions through a chip of graphene under the effect of magnetic field and a time vibrating double barrier with frequency $w$ is investigated. Quantum interference within the oscillating barrier has an important effect on quasi-particles tunneling. A combination of both a time dependent potential and a magnetic field generate physical states whose energy is double quantified by the pair of integers $(n, l)$ with high degeneracy. The large number of modes that exist in the energy spectrum presents a colossal difficulty in numerical computations. Thus we were obliged to make a truncation and limit ourselves to the central $(n = 0)$ and two adjacent side band ($n=\pm 1$).

cond-mat.mes-hall↗

arXiv2014

Factorization of Dirac Equation and Graphene Quantum Dot

We consider a quantum dot described by a cylindrically symmetric 2D Dirac equation. The potentials representing the quantum dot are taken to be of different types of potential configuration, scalar, vector and pseudo-scalar to enable us to enrich our study. Using various potential configurations, we found that in the presence of a mass term an electrostatically confined quantum dot can accommodate true bound states, which is in agreement with previous work. The differential cross section associated with one specific potential configuration has been computed and discussed as function of the various potential parameters.

cond-mat.mes-hall↗

arXiv2014

Tunneling of Massive Dirac Fermions in Graphene through Time-periodic Potential

The energy spectrum of graphene sheet with a single barrier structure having a time periodic oscillating height and subjected to magnetic field is analyzed. The corresponding transmission is studied as function of the obtained energy and the potential parameters. Quantum interference within the oscillating barrier has an important effect on quasiparticles tunneling. In particular the time-periodic electromagnetic field generates additional sidebands at energies ε+ l\hbar ω(l=0,\pm 1, \cdots) in the transmission probability originating from the photon absorption or emission within the oscillating barrier. Due to numerical difficulties in truncating the resulting coupled channel equations we limited ourselves to low quantum channels, i.e. l=0,\pm 1.

cond-mat.mes-hall↗

arXiv2014

Band Tunneling through Double Barrier in Bilayer Graphene

By taking into account the full four band energy spectrum, we calculate the transmission probability and conductance of electrons across symmetric and asymmetric double potential barrier with a confined interlayer potential difference in bilayer graphene. For energies less than the interlayer coupling γ_{1}, E<γ_1, we have one channel for transmission which exhibits resonances, even for incident particles with energies less than the strength of barriers, E < U_j, depending on the double barrier geometry. In contrast, for higher energies E > γ_{1}, we obtain four possible ways for transmission resulting from the two propagating modes. We compute the associated transmission probabilities as well as their contribution to the conductance, study the effect of the double barrier geometry.

cond-mat.mes-hall↗

arXiv2013

Goos-Hanchen like Shifts in Graphene Double Barriers

We study the Goos-Hanchen like shifts for Dirac fermions in graphene scattered by double barrier structures. After obtaining the solution for the energy spectrum, we use the boundary conditions to explicitly determine the Goos-Hanchen like shifts and the associated transmission probability. We analyze these two quantities at resonances by studying their {main} characteristics as a function of the energy and electrostatic potential parameters. To check the validity of our computations we recover previous results obtained for a single barrier under appropriate limits.

cond-mat.mes-hall↗

arXiv2013

Factorization of Dirac Equation in Two Space Dimensions

We present a systematic approach for the separation of variables for the two-dimensional Dirac equation in polar coordinates. The three vector potential, which couple to the Dirac spinor via minimal coupling, along with the scalar potential are chosen to have angular dependence which emanate the Dirac equation to complete separation of variables. Exact solutions are obtained for a class of solvable potentials along with their relativistic spinor wavefunctions. Particular attention is paid to the situation where the potentials are confined to a quantum dot region and are of scalar, vector and pseudo-scalar type. The study of a single charged impurity embedded in a 2D Dirac equation in the presence of a uniform magnetic field was treated as a particular case of our general study.

math-ph↗

arXiv2013

Graphene Nanoribbon in Sharply Localized Magnetic Fields

We study the effect of a sharply localized magnetic field on the electron transport in a strip (ribbon) of graphene sheet, which allows to give results for the transmission and reflection probability through magnetic barriers. The magnetic field is taken as a single and double delta type localized functions, which are treated later as the zero width limit of gaussian fields. For both field configurations, we evaluate analytically and numerically their transmission and reflection coefficients. The possibility of spacial confinement due to the inhomogeneous field configuration is also investigated.

cond-mat.mes-hall↗

arXiv2012

Confined Dirac Particles in Constant and Tilted Magnetic Field

We study the confinement of charged Dirac particles in 3+1 space-time due to the presence of a constant and tilted magnetic field. We focus on the nature of the solutions of the Dirac equation and on how they depend on the choice of vector potential that gives rise to the magnetic field. In particular, we select a "Landau gauge" such that the momentum is conserved along the direction of the vector potential yielding spinor wavefunctions, which are localized in the plane containing the magnetic field and normal to the vector potential. These wave functions are expressed in terms of the Hermite polynomials. We point out the relevance of these findings to the relativistic quantum Hall effect and compare with the results obtained for a constant magnetic field normal to the plane in 2+1 dimensions.

hep-th↗

arXiv2012

Transport Properties through Double Barrier Structure in Graphene

The mode-dependent transmission of relativistic ballistic massless Dirac fermion through a graphene based double barrier structure is being investigated for various barrier parameters. We compare our results with already published work and point out the relevance of these findings to a systematic study of the transport properties in double barrier structures. An interesting situation arises when we set the potential in the leads to zero, then our 2D problem reduces effectively to a 1D massive Dirac equation with an effective mass proportional to the quantized wave number along the transverse direction. Furthermore we have shown that the minimal conductivity and maximal Fano factor remain insensitive to the ratio between the two potentials V_2/V_1=α.

cond-mat.mes-hall↗

arXiv2011

Solution of One-dimensional Dirac Equation via Poincare Map

We solve the general one-dimensional Dirac equation using a "Poincare Map" approach which avoids any approximation to the spacial derivatives and reduces the problem to a simple recursive relation which is very practical from the numerical implementation point of view. To test the efficiency and rapid convergence of this approach we apply it to a vector coupling Woods--Saxon potential, which is exactly solvable. Comparison with available analytical results is impressive and hence validates the accuracy and efficiency of this method.

hep-th↗

arXiv2009

Confined Dirac Fermions in a Constant Magnetic Field

We obtain an exact solution of the Dirac equation in (2+1)-dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. The solution space consists of a positive and negative energy solution, each of which splits into two disconnected subspaces depending on the sign of an azimuthal quantum number, k = 0, \pm 1, \pm 2,... and whether the cyclotron frequency is larger or smaller than the oscillator frequency. The spinor wavefunction is written in terms of the associated Laguerre polynomials. For negative k, the relativistic energy spectrum is infinitely degenerate due to the fact that it is independent of k. We compare our results with already published work and point out the relevance of these findings to a systematic formulation of the relativistic quantum Hall effect in a confining potential.

hep-th↗