arXiv subjects

Abderrahim El Mouhafid

Publications and source records attributed to Abderrahim El Mouhafid.

16 recordsLinked to original sources

arXiv2024

Transport properties through alternating borophene and graphene superlattices

The electronic transport properties of two junctions (BGB, GBG) made of borophene (B) and graphene (G) are investigated. Using the transfer matrix method with Chebyshev polynomials, we have studied single and multiple barriers in a superlattice configuration. We showed that a single barrier exhibits remarkable tilted transport properties, with perfect transmission observed for both junctions under normal incidence. We found that robust superlattice transmission is maintained for multiple barriers, particularly in the BGB junction. It turns out that by varying the incident energy, many gaps appear in the transmission probability. The number, width, and position of these transmission gaps can be manipulated by adjusting the number of cells, incident angle, and barrier characteristics. For diffuse transport, we observed considerable variations in transmission probability, conductance and the Fano factor, highlighting the sensitivity of these junctions to the physical parameters. We showed different behaviors between BGB and GBG junctions, particularly with respect to the response of conductance and Fano factor when barrier height varies. For ballistic transport, we have seen that the minimum {scaled conductance} is related to the maximum Fano factor, demonstrating their control under specific conditions of the physical parameters. Analysis of the length ratio (geometric factor) revealed some remarkable patterns, where {scaled conductance} and the Fano factor converged to certain values as the ratio approached infinity.

cond-mat.mes-hall↗

arXiv2024

Transmissions in gapped graphene exposed to tilting and oscillating barriers

We investigate the transmissions of fermions through gapped graphene structures by employing a combination of double barrier tilting and a time-oscillating potential. The latter introduces additional sidebands into the transmission probability, which manifest at energy levels determined by the frequency and incident energy. These sidebands arise from the absorption or emission of photons generated by the oscillating potential. We demonstrate that the tilting and positioning of the scattering events within the barriers play a crucial role in determining the peak of tunneling resistance. In particular, the presence of a mid-barrier-embedded scatter leads to a transition from a peak to a cusp when the incident energy reaches the Dirac point within a barrier. Additionally, we illustrate that introducing a time-varying potential results in transmissions dispersing across both the central band and the sidebands.

cond-mat.mes-hall↗

arXiv2024

Tunneling in ABC trilayer graphene superlattice

We study the transport properties of Dirac fermions in ABC trilayer graphene (ABC-TLG) superlattices. More specifically, we analyze the impact of varying the physical parameters -- the number of cells, barrier/well width, and barrier heights -- on electron tunneling in the ABC-TLG. In the initial stage, we solved the eigenvalue equation to determine the energy spectrum solutions for the ABC-TLG superlattices. Subsequently, we applied boundary conditions to the eigenspinors and employed the transfer matrix method to calculate transmission probabilities and conductance. For the two-band model, we identified the presence of Klein tunneling, with a notable decrease as the number of cells increased. The introduction of interlayer bias opened a gap as the number of cells increased, accompanied by an asymmetry in scattered transmission. Increasing the barrier/well width and the number of cells resulted in an amplified number of gaps and oscillations in both two-band and six-band cases. We observed a corresponding decrease in conductance as the number of cells increased, coinciding with the occurrence of a gap region. Our study demonstrates that manipulating parameters such as the number of cells, the width of the barrier/well, and the barrier heights provides a means of controlling electron tunneling and the occurrence of gaps in ABC-TLG. Specifically, the interplay between interlayer bias and the number of cells is identified as a crucial factor influencing gap formation and transmission asymmetry.

cond-mat.mes-hall↗

arXiv2024

Transport properties in ABC-ABA-ABC trilayer graphene junctions

Trilayer graphene {(TLG)} consists of three layers of graphene arranged in a particular stacking order. In the case of ABC-ABA-ABC stacking, the layers are arranged in an A-B-C sequence, followed by an A-B-A sequence, and again an A-B-C sequence. This stacking arrangement introduces specific electronic properties and band structures due to the different stacking configurations. We focus on elucidating the transport properties of a p-n-p junction formed with ABC-ABA-ABC stacking TLG. Employing the transfer matrix method and considering continuity conditions at the junction boundaries, we establish transmission and reflection probabilities, along with conductance. Notably, electron transport through the ABC-ABA-ABC junction exhibits Klein tunneling, resulting in substantial conductance even in the absence of a potential barrier $V_0$. This effect arises from the effective barrier induced by our specific stacking, facilitating the passage of a maximal number of electrons. However, the presence of $V_0$ diminishes Klein tunneling, leading to conductance minima. Furthermore, our findings highlight that interlayer bias $δ$ induces a hybridization of the linear and parabolic bands of ABA-TLG within the junction, reducing resonances. In cases where $δ\neq0$ and $V_0\neq0$, we observe a suppression of the gap, contrary to the results obtained in ABC tunneling studies where a gap exists.

cond-mat.mes-hall↗

arXiv2024

Effect of a perpendicular magnetic field on bilayer graphene under dual gating

By studying the impact of a perpendicular magnetic field $B$ on AB-bilayer graphene (AB-BLG) under dual gating, we yield several key findings for the ballistic transport of gate $U_\infty$. Firstly, we discover that the presence of $B$ leads to a decrease in transmission. At a high value of $B$, we notice the occurrence of anti-Klein tunneling over a significant area. Secondly, in contrast to the results reported in the literature, where high peaks were found with an increasing in-plane pseudomagnetic field applied to AB-BLG, we find a decrease in conductivity as $B$ increases. However, it is worth noting that in both cases, the number of oscillations decreases compared to the result in the study where no magnetic field was present $(B = 0)$. Thirdly, at the neutrality point, we demonstrate that the conductivity decreases and eventually reaches zero for a high value of $B$, which contrasts with the result that the conductivity remains unchanged regardless of the value taken by the in-plane field. Finally, we consider the diffusive transport with gate $U_\infty = 0.2 γ_1$ and observe two scenarios. The amplitude of conductivity oscillations increases with $B$ for energy $E$ less than $U_\infty$ but decreases in the opposite case $E>U_\infty$.

cond-mat.mes-hall↗

arXiv2022

Effect of parallel magnetic field on Klein tunneling in $pn$ and $pnp$ graphene trilayer junctions

The effect of a parallel magnetic field $B$ and a potential substrate on the transmission, conductivity, and Fano factor of a biased ABC-stacked $pn$ and $pnp$ trilayer graphene junction (ABC-TLG) is investigated theoretically at low energy. We discovered that, in the presence of a high magnetic field $B=1400$T, the ABC-TLG can exhibit new Klein tunneling at two new incidence $k_y$ values, in addition to the usual value of $k_y=0$ and whatever the energy value is. Indeed, the transmission of ABC-TLG via $ pn $ and $ pnp $ junctions is transformed into a three-separate transmission of single-like graphene (SLG), with Klein tunneling appearing at $k_y=0$ and $k_y=\pmκ$ ($κ$ is highly dependent on $B$). Furthermore, the conductivity $σ$ and Fano factor $F$ behave similarly to SLG, with ABC-TLG having the lowest $σ=3g_0/π$ and highest $F=1/3$ at $B=1400$T and $σ_{\text{TLG}}=3σ_{\text{SLG}}$.

cond-mat.mes-hall↗

arXiv2022

Klein tunneling through triple barrier in AB bilayer graphene

We investigate the transport properties of charge carriers in AB bilayer graphene through a triple electrostatic barrier. We calculate the transmission and reflection using the continuity conditions at the interfaces of the triple barrier together with the transfer matrix method. First, we consider the case where the energy is less than the interlayer coupling $γ_1$ and show that, at normal incidence, transmission is completely suppressed in the gap for a large barrier width while it appears in the gap for a small barrier width. For energies greater than $γ_1$, we show that in the absence of an interlayer potential difference, transmission is less than that of a single barrier, but in its presence, transmission in the gap region is suppressed, as opposed to a double barrier. It is found that one, two, or three gaps can be created depending on the number of interlayer potential differences applied. Resonance in the $T_-^+$ transmission channel is observed that is not seen in the single and double barrier cases. Finally, we compute the conductance and show that the number of peaks is greater than the double barrier case.

cond-mat.mes-hall↗

arXiv2021

Klein tunneling through double barrier in ABC-trilayer graphene

Klein tunneling and conductance for Dirac fermions in ABC-stacked trilayer graphene (ABC-TLG) through symmetric and asymmetric double potential barriers are investigated using the two and six-band continuum model. Numerical results for our system show that the transport is sensitive to the height, the width and the distance between the two barriers. Klein paradox at normal incidence and resonant features at non-normal incidence in the transmission result from resonant electron states in the wells or hole states in the barriers and strongly influence the ballistic conductance of the structures.

cond-mat.mes-hall↗

arXiv2021

Transport Properties in Gapped Bilayer Graphene

We investigate transport properties through a rectangular potential barrier in AB-stacked bilayer graphene (AB-BLG) gapped by dielectric layers. Using the Dirac-like Hamiltonian with a transfer matrix approach we obtain transmission and reflection probabilities as well as the associated conductance. For two-band model and at normal incidence, we find extra resonances appearing in transmission compared to biased AB-BLG, which are Fabry-Pérot resonance type. Now by taking into account the inter-layer bias, we show that both of transmission and anti-Klein tunneling are diminished. Regarding four band model, we find that the gap suppresses transmission in an energy range by showing some behaviors look like "Mexican hats". We examine the total conductance and show that it is affected by the gap compared to AA-stacked bilayer graphene. In addition, we find that the suppression in conductance is more important than that for biased AB-BLG.

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↗

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↗

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

Transport Properties for Triangular Barriers in Graphene

We theoretically study the electronic transport properties of Dirac fermions through one and double triangular barriers in graphene. Using the transfer matrix method, we determine the transmission, conductance and Fano factor. They are obtained to be various parameters dependent such as well width, barrier height and barrier width. Therefore, different discussions are given and comparison with the previous significant works is done. In particular, it is shown that at Dirac point the Dirac fermions always own a minimum conductance associated with a maximum Fano factor and change their behaviors in an oscillatory way (irregularly periodical tunneling peaks) when the potential of applied voltage is increased.

cond-mat.mes-hall↗

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

Massless Dirac Fermions in Electromagnetic Field

We study the relations between massless Dirac fermions in an electromagnetic field and atoms in quantum optics. After getting the solutions of the energy spectrum, we show that it is possible to reproduce the 2D Dirac Hamiltonian, with all its quantum relativistic effects, in a controllable system as a single trapped ion through the Jaynes--Cummings and anti-Jaynes--Cummings models. Also we show that under certain conditions the evolution of the Dirac Hamiltonian provides us with Rashba spin-orbit and linear Dresselhaus couplings. Considering the multimode multiphoton Jaynes-Cummings model interacting with N modes of electromagnetic field prepared in general pure quantum states, we analyze the Rabi oscillation. Evaluating time evolution of the Dirac position operator, we determine the Zitterbewegung frequency and the corresponding oscillating term as function of the electromagnetic field.

hep-th↗

arXiv2010

Dirac Fermions in Inhomogeneous Magnetic Field

We study a confined system of Dirac fermions in the presence of inhomogeneous magnetic field. Splitting the system into different regions, we determine their corresponding energy spectrum solutions. We underline their physical properties by considering the conservation energy where some interesting relations are obtained. These are used to discuss the reflexion and transmission coefficients for Dirac fermions and check the probability condition for different cases. We generalize the obtained results to a system with gap and make some analysis. After evaluating the current-carrying states, we analyze the Klein paradox and report interesting discussions.

cond-mat.mes-hall↗