arXiv subjects

Ahmed Jellal

Publications and source records attributed to Ahmed Jellal.

At least 127 records · Page 7Linked to original sources

arXiv2018

Transport Properties in Graphene Superlattices

Using Chebyshev polynomials, we study the electronic transport properties of massless Dirac fermions in symmetrical graphene superlattice composed of three regions. Matching wavefunctions and using transfer matrix method, we explicitly determine transmission probability as well as the conductance and Fano factor. At vertical Dirac points, we numerically find that the transmission probability shows transmission gaps, conductance has minimums and Fano factor has maximums.

cond-mat.mes-hall↗

arXiv2018

Time-Dependent Strain in Graphene

We will analyse the effect of time-dependent strain on a sheet of graphene by using the field theory approach. It will be demonstrated that in the continuum limit, such a strain will induce a non-abelian gauge field in graphene. We will analyse the effective field theory of such system near the Dirac points and study its topological properties.

cond-mat.mes-hall↗

arXiv2018

Electron Scattering in Gapped Graphene Quantum Dots

Due to Klein tunneling in graphene only quasi-bound states are realized in graphene quantum dots by electrostatic gating. Particles in the quasi-bound states are trapped inside the dot for a finite time and they keep bouncing back and forth till they find their way out. Here we study the effect of an induced gap on the scattering problem of Dirac electrons on a circular electrostatically confined quantum dot. Introducing an energy gap inside the quantum dot enables us to distinguish three scattering regimes instead of two in the case of gapless graphene quantum dot. We will focus on these regimes and analyze the scattering efficiency as a function of the electron energy, the dot radius and the energy gap. Moreover, we will discuss how the system parameters can affect the scattering resonances inside the dot.

cond-mat.mes-hall↗

arXiv2018

Purity Temperature Dependent for Coupled Harmonic Oscillators

We consider the thermal aspect of a system composed of two coupled harmonic oscillators and study the corresponding purity. We initially consider a situation where the system is brought to a canonical thermal equilibrium with a heat-bath at temperature $T$. We adopt the path integral approach and introduce the evolution operator to calculate the density matrix and subsequently the reduced matrix density. It is used to explicitly determine the purity in terms of different physical quantities and therefore study some limiting cases related to temperature as well as other parameters. Different numerical results are reported and discussed in terms of the involved parameters of our system.

quant-ph↗

arXiv2018

Thermodynamics Properties of Confined Particles on Noncommutative Plane

We consider a system of $N$ particles living on the noncommutative plane in the presence of a confining potential and study its thermodynamics properties. Indeed, after calculating the partition function, we determine the corresponding internal energy and heat capacity where different corrections are obtained. In analogy with the magnetic field case, we define an effective magnetization and study its susceptibility in terms of the noncommutative parameter $θ$. By introducing the chemical potential, we investigate the Bose-Einstein condensation for the present system. Different limiting cases related to the temperature and $θ$ will be analyzed as well as some numerical illustration will be presented.

cond-mat.stat-mech↗

arXiv2017

Band Structures of Symmetrical Graphene Superlattice with Cells of three Regions

We study the electronic band structures of massless Dirac fermions in symmetrical graphene superlattice with cells of three regions. Using the transfer matrix method, we explicitly determine the dispersion relation in terms of different physical parameters. We numerically analyze such relation and show that there exist three zones: bound, unbound and forbidden states. In the central zone of the band structures, we determine and enumerate the vertical Dirac points, opening gaps and additional Dirac points. Finally, we inspect the potential effect on minibands, the anisotropy of group velocity and the energy bands contours near Dirac points. We also discuss the evolution of gap edges and cutoff region near the vertical Dirac points.

cond-mat.mes-hall↗

arXiv2017

Energy Levels of Quantum Ring in ABA-Stacked Trilayer Graphene

We present the solutions of the energy spectrum of charge carriers confined in quantum ring in ABA-stacked trilayer graphene subjected to a perpendicular magnetic field. The calculations were performed in the context of the continuum model by solving the Dirac equation for a zero width ring geometry, i.e. freezing out the carrier radial motion. We show that the obtained energy spectrum exhibits different symmetries with respect to the magnetic field and other parameters. The application of a potential shift the energy spectrum vertically while the application of a magnetic field breaks all symmetries. We compare our results with those of of the ideal quantum ring in monolayer and bilayer graphene.

cond-mat.mes-hall↗

arXiv2017

Exact Green Function for Neutral Pauli-Dirac Particle with Anomalous Magnetic Momentum in Linear Magnetic Field

We consider Pauli--Dirac fermion submitted to an inhomogeneous magnetic field. It is showed that the propagator of the neutral Dirac particle with an anomalous magnetic moment in an external linear magnetic field is the causal Green function $S^{c}(x_{b},x_{a})$ of the Pauli--Dirac equation. The corresponding Green function is calculated via path integral method in global projection, giving rise to the exact eigenspinors expressions. The neutral particle creation probability corresponding to our system is analyzed, which is obtained as function of the introduced field $B'$ and the additional spin magnetic moment $μ$.

hep-th↗

arXiv2016

Multibands Tunneling in AAA-Stacked Trilayer Graphene

We study the electronic transport through np and npn junctions for AAA-stacked trilayer graphene. Two kinds of gates are considered where the first is a single gate and the second is a double gate. After obtaining the solutions for the energy spectrum, we use the transfer matrix method to determine the three transmission probabilities for each individual cone $τ=0, \pm 1$. We show that the quasiparticles in AAA-stacked trilayer graphene are not only chiral but also labeled by an additional cone index $τ$. The obtained bands are composed of three Dirac cones that depend on the chirality indexes. We show that there is perfect transmission for normal or near normal incidence, which is a manifestation of the Klein tunneling effect. We analyze also the corresponding total conductance, which is defined as the sum of the conductance channels in each individual cone. Our results are numerically discussed and compared with those obtained for ABA- and ABC-stacked trilayer graphene.

cond-mat.mes-hall↗

arXiv2016

Energy Levels of an Ideal Quantum Ring in AA-Stacked Bilayer Graphene

We theoretically analyze the energy spectrum of a quantum ring in AA-stacked bilayer graphene with radius $R$ for a zero width subjected to a perpendicular magnetic field $B$. An analytical approach, using the Dirac equation, is implemented to obtain the energy spectrum by freezing out the carrier radial motion. The obtained spectrum exhibits different symmetries and for a fixed total angular momentum $m$, it has a hyperbolic dependence of the magnetic field. In particular, the energy spectra are not invariant under the transformation $B \longrightarrow -B$. The application of a potential, on the upper and lower layer, allows to open a gap in the energy spectrum and the application of a non zero magnetic field breaks all symmetries. We also analyze the basics features of the energy spectrum to show the main similarities and differences with respect to ideal quantum ring in monolayer, AB-stacked bilayer graphene and a quantum ring with finite width in AB-stacked bilayer graphene.

cond-mat.mes-hall↗

arXiv2016

Tunneling of Graphene Massive Dirac Fermions through a Double Barrier

We study the tunneling of Dirac fermions in graphene through a double barrier potential allowing the carriers to have an effective mass inside the barrier as generated by a lattice miss-match with the boron nitride substrate. The consequences of this gap opening on the transmission are investigated. The realization of resonant tunneling conditions is also analyzed.

cond-mat.mes-hall↗

arXiv2016

Electrostatic and Magnetic Fields in Bilayer Graphene

We compute the transmission probability through rectangular potential barriers and p-n junctions in the presence of a magnetic and electric fields in bilayer graphene taking into account contributions from the full four bands of the energy spectrum. For energy $E$ higher than the interlayer coupling $γ_1$ ($E > γ_1$) two propagation modes are available for transport giving rise to four possible ways for transmission and reflection coefficients. However, when the energy is less than the height of the barrier the Dirac fermions exhibit transmission resonances and only one mode of propagation is available for transport. We study the effect of the interlayer electrostatic potential denoted by $δ$ and variations of different barrier geometry parameters on the transmission probability.

cond-mat.mes-hall↗

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

Confined System with Rashba Coupling in Constant Magnetic Field

We study a two dimensional system of electrons with Rashba coupling in the constant magnetic field $B$ and confining potential. We algebraically diagonalize the corresponding Hamiltonian to end up with the solutions of the energy spectrum. In terms of two kinds of operator we construct two symmetries and discuss the filling of the shells with electrons for strong and weak $B$. Subsequently, we show that our system is sharing some common features with quantum optics where the exact operator solutions for the basics Jaynes-Cummings variables are derived from our results. An interesting limit is studied and the corresponding quantum dynamics is recovered.

cond-mat.mes-hall↗

arXiv2016

Path Integral Confined Dirac Fermions in a Constant Magnetic Field

We consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a symmetric global projection, which provides a symmetric form for the Green function. Based on this, we show that it is possible to end up with the propagator of the harmonic oscillator for one charged particle. After some transformations, we derive the normalized wave functions and the eigenvalues in terms of different physical parameters and quantum numbers. By interchanging quantum numbers, we show that our solutions possed interesting properties. The density of current and the non-relativistic limit are analyzed where different conclusions are obtained.

hep-th↗

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↗

arXiv2016

AA-stacked Bilayer Graphene Quantum Dots in Magnetic Field

By applying the infinite-mass boundary condition, we analytically calculate the confined states and the corresponding wave functions of AA-stacked bilayer graphene quantum {dots} in the presence of an uniform magnetic field $B$. It is found that the energy spectrum shows two set of levels, which are the double copies of the energy spectrum for single layer graphene, shifted up-down by $+γ$ and $-γ$, respectively. However, the obtained spectrum exhibits different symmetries between the electron and hole states as well as the intervalley symmetries. It is noticed that, the applied magnetic field breaks all symmetries, except one related to the intervalley electron-hole symmetry, i.e. $E^e(τ,m)=-E^h(τ,m)$. Two different regimes of confinement are found: the first one is due to the infinite-mass barrier at weak $B$ and the second is dominated by the magnetic field as long as $B$ is large. We numerically investigated the basics features of the energy spectrum to show the main similarities and differences with respect to monolayer graphene, AB-stacked bilayer graphene and semiconductor quantum dots.

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↗