arXiv subjects

Ahmed Jellal

Publications and source records attributed to Ahmed Jellal.

At least 109 records · Page 6Linked to original sources

arXiv2020

Electronic Properties of Graphene Quantum Ring with Wedge Disclination

We study the energy spectrum and persistent current of charge carriers confined in a graphene quantum ring geometry of radius $R$ and width $w$ subjected to a magnetic flux. We consider the case where the crystal symmetry is locally modified by replacing a hexagon by a pentagon, square, heptagon or octagon. To model this type of defect we include appropriate boundary conditions for the angular coordinate. The electrons are confined to a finite width strip in radial direction by setting infinite mass boundary conditions at the edges of the strip. The solutions are expressed in terms of Hankel functions and their asymptotic behavior allows to derive quantized energy levels in the presence of an energy gap. We also investigate the persistent currents that appear in the quantum ring and how wedge disclination influences different quantum transport quantities.

cond-mat.mes-hall↗

arXiv2020

Goos-Hänchen Shifts in Gapped Graphene subject to External Fields

We study Dirac fermions in gapped graphene that are subjected to a magnetic field and a potential barrier harmonically oscillating in time. The tunneling modes inside the gap and the associated Goos-Hänchen (GH) shifts are analytically investigated. We show that the GH shifts in transmission for the central band and the first two sidebands change sign at the Dirac points $ε+l\hbar\tildeω$ $(l=0,\pm 1)$. We also find that the GH shifts can be either negative or positive and becomes zero at transmission resonances.

cond-mat.mes-hall↗

arXiv2020

Confinement in Gapped Graphene with Magnetic Flux

We study the propagation of electrons in a circular quantum dot of gapped graphene subject to the magnetic flux $ϕ$. We present analytical expressions for the eigenstates, scattering coefficients, scattering efficiency and radial component of the reflected current. We identify different scattering regimes as a function of the physical parameters such as the incident electronic energy, potential barrier, radius of quantum dot, gap and $ϕ$. We choose two values of the flux $ϕ=1/2, 3/2$ and show that for low energy of the incident electron, the scattering resonances appear and the far-field scattered current presents distinct preferred scattering directions.

cond-mat.mes-hall↗

arXiv2020

Measuring Space Deformation via Graphene under Constraints

We describe the lattice deformation in graphene under strain effect by considering the spacial-momenta coordinates do not commute. This later can be realized by introducing the star product to end up with a generalized Heisenberg algebra. Within such framework, we build a new model describing Dirac fermions interacting with an external source that noncommutative parameter $κ$ dependent. The solutions of the energy spectrum are showing effective Landau levels in similar way to the case of a real magnetic field applied to graphene. We show that some strain configurations would be able to explicitly evaluate $κ$ and then offer a piste toward its measurement.

cond-mat.mes-hall↗

arXiv2020

Zitterbewegung Effect in Graphene with Spacially Modulated Potential

The Zitterbewegung (ZB) effect is investigated in graphene with spacially modulated potential near the original Dirac point (ODP) and extra Dirac points (EDPs). Our calculations show that to get the large ZB oscillations, the wave packet center must be at the angle $θ_0=0$ for EDPs located at zero-energy, or $θ_0=π/2$ for both ODP and EDPs at finite energy $\varepsilon=mπ$ ($m$ integer). By varying the parameters ($q_2, \mathbb{V}$) of the periodic potential and the initial momentum ($κ_0, θ_0$) of Gaussian wave packet, it is found that the frequency of the ZB oscillations is in the range $[10^{7}~\text{Hz}, 10^{13}~\text{Hz}$] depending on what type of EDP is generated and the amplitude reaches hundreds of angstroms but their attenuation becomes very slow. More analysis of the frequency shows the possibilities in experimentally realizing the ZB effect in our system.

cond-mat.mes-hall↗

arXiv2020

Energy Levels of Graphene Magnetic Circular Quantum Dot

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 different regions composing our system. Using the continuum model and applying boundary conditions at the interface, we obtain analytical results for the energy levels. The dependence of the energy levels on the quantum dot radius, magnetic field and electrostatic potential is analyzed for the two valleys $K$ and $K'$. We show that the energy levels exhibit characteristics of interface states and have an energy gap.

cond-mat.mes-hall↗

arXiv2020

Time-dependent Goos-Hänchen Shifts in Gapped Graphene

We study the Goos-Hänchen (GH) shifts for transmitted Dirac fermions in gapped graphene through a single barrier structure having a time periodic oscillating component. Our analysis shows that the GH shifts in transmission for central band $l=0$ and two first sidebands $l=\pm1$ change sign at the Dirac points $E=V+l\hbarω$. In particular the GH shifts inbtransmission exhibit enhanced peaks at each bound state associated with the single barrier when the incident angle is less than the critical angle associated with total reflection. Klein tunneling, reflected by perfect transmission at normal incidence, is also preserved in the presence of an oscillating barrier.

cond-mat.mes-hall↗

arXiv2019

Entanglement in Three Coupled Harmonic Oscillators

We develop an approach in solving exactly the problem of three-body oscillators including general quadratic interactions in the coordinates for arbitrary masses and couplings. We introduce a unitary transformation of three independent angles to end up with a diagonalized Hamiltonian. Using the representation theory of the group $SU(3)$, we explicitly determine the solutions of the energy spectrum. Considering the ground state together with reduced density matrix, we derive the corresponding purity function that is giving rise to minimal and maximal entanglement under suitable conditions. The cases of realizing one variable among three is discussed and know results in literature are recovered.

quant-ph↗

arXiv2019

Low Energy Consequences of Loop Quantum Gravity

As the loop quantum gravity is based on polymer quantization, we will argue that the polymer length (like string length) can be several orders larger than the Planck length, and this can have low energy consequences. We will demonstrate that a short distance modification of a quantum system by polymer quantization and by string theoretical considerations can produce similar behavior. Moreover, it will be demonstrated that a family of different deformed Heisenberg algebras can produce similar low energy effects. We will analyze such polymer correction to a degenerate Fermi gases in a harmonic trap, and its polymer corrected thermodynamics.

hep-th↗

arXiv2019

Goos-Hänchen Shifts in Graphene with Spatially Modulated Potential

Using the energy spectrum of graphene with spatially modulated potential, we study the Goos-Hänshen shifts near extra Dirac points located at finite energy $\varepsilon=mπ$, with $m$ integer. On both sides of such points, we show that the Goos-Hänshen shifts can be negative as well as positive under various conditions. It is found that the shifts are strongly depending on the effects of the incident energy, potential height, incident angle and width of central region of unit cell. Such effects tell us that such width can be used to tune the shifts at the extra Dirac points.

cond-mat.mes-hall↗

arXiv2019

Electronic Structure of Graphene with two Strains and Double Barrier

We study the electronic structure of Dirac fermions scattered by double barrier potential in graphene under strain effect. We show that traction and compression strains can be used to generate fermion beam collimation, 1D channels, surface states and confinement. The corresponding transmission probability and conductance at zero temperature are calculated and their numerical implementations taking into account different configurations of physical parameters enabled us to analyze some features of the system.

cond-mat.mes-hall↗

arXiv2019

Magnetic Field Effect on Strained Graphene Junctions

We investigate the spin-dependent transport properties of a ferromagnetic/strained/normal graphene junctions with central region subjected to a magnetic field $B$. An analytical approach, based on Dirac equation, is implemented to obtain the eigenstates and eigenvalues of the charge carrier in three regions. Using the transfer matrix method, we determine the spin-dependent transmission in the presence of an applied strain along the armchair and zigzag directions of the graphene sample. We find that the strain remarkably modifies the Landau levels (LLs) originating from the applied $B$. It is shown that the spin up/down energy bands, in the first region, are shifted by the exchange $H_{ex}$ and left the whole spectrum linear as in the case of pristine graphene. In the central region, the position of the Dirac point changes due to the uniaxial strain and $B$. It is also found that the uniaxial strain in graphene induces a contraction of the LLs spectra. Moreover, the strain and $B$ modify the shape and position of some peaks in the transmission probabilities.

cond-mat.mes-hall↗

arXiv2019

Transmission in Graphene through Time-oscillating Linear Barrier

Transmission probabilities of Dirac fermions in graphene under linear barrier potential oscillating in time are investigated. Solving Dirac equation we end up with the solutions of the energy spectrum depending on several modes coming from the oscillations. These will be used to obtain a transfer matrix that allows to determine transmission amplitudes of all modes. Due to numerical difficulties in truncating the resulting coupled channel equations, we limit ourselves to low quantum channels, i.e. $l = 0, \pm1$, and study the three corresponding transmission probabilities.

cond-mat.mes-hall↗

arXiv2019

Effect of Magnetic Field on Goos-Hänchen Shifts in Gaped Graphene Triangular Barrier

We study the effect of a magnetic field on Goos-Hänchen shifts in gaped graphene subjected to a double triangular barrier. Solving the wave equation separately in each region composing our system and using the required boundary conditions, we then compute explicitly the transmission probability for scattered fermions. These wavefunctions are then used to derive the Goos-Hänchen shifts in terms of different physical parameters such as energy, electrostatic potential strength and magnetic field. Our numerical results show that the Goos-Hänchen shifts are affected by the presence of the magnetic field and depend on the geometrical structure of the triangular barrier.

cond-mat.mes-hall↗

arXiv2019

Thermodynamic Properties of Graphene in Magnetic Field and Rashba Coupling

We study the thermodynamic properties of massless Dirac fermions in graphene subjected to a uniform magnetic field $B$ together with Rashba coupling parameter $λ_R$. The thermodynamic functions such as the Helmholtz free energy, total energy, entropy and heat capacity are obtained in the high temperature regime using an approach based on the zeta function. These functions will be numerically examined by considering two cases related to $λ_R$ smaller or greater than $B$. In particular, we show that the Dulong-Petit law is verified for both cases.

cond-mat.mes-hall↗

arXiv2019

Band structure and Klein paradox for a pn junction in ABCA-tetralayer graphene

We investigate the band structure of ABCA-tetralayer graphene (ABCA-TTLG) subjected to an external potential $V$ applied between top and bottom layers. Using the tight-binding model, including the nearest $t$ and next-nearest-neighbor $t'$ hopping, low-energy model and two-band approximation model we study the band structure variation along the lines $Γ-M-K-Γ$ in the first Brillouin zone, electronic band gap near Dirac point $K$ and transmission properties, respectively. Our results reveal that ABCA-TTLG exhibits markedly different properties as functions of $t'$ and $V$. We show that the hopping parameter $t'$ changes the energy dispersion, the position of $K$ and breaks sublattice symmetries. A sizable band gap is created at $K$, which could be opened and controlled by the applied potential $V$. This gives rise to 1D-like van Hove singularities (VHS) in the density of states (DOS). We study the relevance of the skew hopping parameters $γ_3$ and $γ_4$ to these properties and show that for energies $E\gtrsim6$meV their effects are negligible. Our results are numerically discussed and compared with the literature.

cond-mat.mes-hall↗

arXiv2019

Entropies for Coupled Harmonic Oscillators and Temperature

We study two entropies of a system composed of two coupled harmonic oscillators which is brought to a canonical thermal equilibrium with a heat-bath at temperature $T$. Using the purity function, we explicitly determine the Rényi and van Newmon entropies in terms of different physical parameters. We will numerically analyze these two entropies under suitable conditions and show their relevance.

quant-ph↗

arXiv2018

Goos-Hänchen Shifts in Graphene-Based Linear Barrier

Using the energy spectrum of a system made of graphene subjected to a linear barrier potential, we study the Goos-Hänshen shifts. The calculation is done by first determining the corresponding phase shifts via the transmission and reflection probabilities. Numerical analysis shows that the Goos-Hänshen shifts depend strongly on the incident energy, barrier height and width, and vary positively or negatively under suitable conditions.

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