arXiv subjects

Hocine Bahlouli

Publications and source records attributed to Hocine Bahlouli.

At least 37 records · Page 2Linked to original sources

arXiv2022

Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene

We study the magnetic field induced Hofstadter butterfly in twisted bilayer graphene (TBG) in various kinds of situations. First, we study the equilibrium case and identify the interlayer hopping processes that are most crucial for the appearance of a Hofstadter butterfly. Surprisingly, the hopping processes that are important for the appearance of the Hofstadter butterfly can be categorized as AA stacking type - that is interlayer hoppings between equivalent sublattices. This is in contrast to AB/BA-type hoppings that are important for the appearance of flat bands in magic angle TBG and were discussed in [Phys. Rev. Lett. 122, 106405 (2019)]. We also find that if AB-type interlayer-hopping processes are turned off the resulting model is chiral but differs from the model discussed in \cite{Tarnopolsky}. Therefore, TBG has two separate chiral limits - one of them is important to understand the formation of flat bands and the other for the Hofstadter butterfly. Taking this as motivation we discuss how the role of AA-type hoppings in combination with lattice relaxation effects can make individual Landau levels slightly harder to resolve in an experimental setting than one would expect from a non-relaxed lattice setting. Finally, we consider the impact of different forms of light on the fractal structure of the butterfly. Particularly, we study the impact of circularly polarized light and longitudinal light originating from a waveguide. As the system is exposed to circularly polarized light we find butterflies with increasingly pronounced asymmetry with respect to energy $E=0$. This is due to the introduction of a gap term that breaks the chiral symmetries for both of the two chiral limits mentioned above. Lastly, we study the effect of longitudinal light that can be produced at the exit of a waveguide, in a slightly simplified model. Here, we find ...

cond-mat.mes-hall↗

arXiv2021

Floquet engineering and non-equilibrium topological maps in twisted trilayer graphene

Motivated by the recent experimental realization of twisted trilayer graphene and the observed superconductivity that is associated with its flat bands at specific angles, we study trilayer graphene under the influence of different forms of light in the non-interacting limit. Specifically, we study four different types of stacking configurations with a single twisted layer. In all four cases, we study the impact of circularly polarized light and longitudinal light coming from a waveguide. We derive effective time-independent Floquet Hamiltonians and review light-induced changes to the band structure. For circularly polarized light, we find band flattening effects as well as band gap openings. We emphasize that there is a rich band topology, which we summarize in Chern number maps that are different for all four studied lattice configurations. The case of a so-called ABC stacking with top layer twist is especially rich and shows a different phase diagram depending on the handedness of the circularly polarized light. Consequently, we propose an experiment where this difference in typologies could be captured via optical conductivity measurements. In contrast for the case of longitudinal light that is coming from a waveguide, we find that the band structure is very closely related to the equilibrium one but the magic angles can be tuned in-situ by varying the intensity of the incident beam of light.

cond-mat.mes-hall↗

arXiv2021

Tunneling of Electrons in Graphene via Double Triangular Barrier in External Fields

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. Solving our Dirac-like equation and matching the solutions at the boundaries allowed us to express our transmission and reflection coefficients in terms of transfer matrix. We show in particular that the transmission exhibits oscillation resonances that are manifestations of the Klein tunneling effect. The triangular barrier electrostatic field was found to play a key role in controlling the peak of tunneling resistance. However, it only slightly modifies the resonances at oblique incidence and leaves Klein paradox unaffected at normal incidence.

cond-mat.mes-hall↗

arXiv2021

Tunneling in an anisotropic cubic Dirac semi-metal

Motivated by a recent first principles prediction of an anisotropic cubic Dirac semi-metal in a real material Tl(TeMo)$_3$, we study the behavior of electrons tunneling through a potential barrier in such systems. To clearly investigate effects from different contributions to the Hamiltonian we study the model in various limits. First, in the limit of a very thin material where the linearly dispersive $z$-direction is frozen out at zero momentum and the dispersion in the $x$-$y$ plane is rotationally symmetric. In this limit we find a Klein tunneling reminiscent of what is observed in single layer graphene and linearly dispersive Dirac semi-metals. Second, an increase in thickness of the material leads to the possibility of a non-zero momentum eigenvalue $k_z$ that acts as an effective mass term in the Hamiltonian. We find that these lead to a suppression of Klein tunneling. Third, the inclusion of an anisotropy parameter $λ\neq 1$ leads to a breaking of rotational invariance. Furthermore, we observed that for different values of incident angle $θ$ and anisotropy parameter $λ$ the Hamiltonian supports different numbers of modes propagating to infinity. We display this effect in form of a diagram that is similar to a phase diagram of a distant detector. Fourth, we consider coexistence of both anisotropy and non-zero $k_z$ but do not find any effect that is unique to the interplay between non-zero momentum $k_z$ and anisotropy parameter $λ$. Last, we studied the case of a barrier that was placed in the linearly dispersive direction and found Klein tunneling $T-1\propto θ^6+\mathcal{O}(θ^8)$ that is enhanced when compared to the Klein tunneling in linear Dirac semi-metals or graphene where $T-1\propto θ^2+\mathcal{O}(θ^4)$.

cond-mat.mes-hall↗

arXiv2020

J-matrix method of scattering for inverse-square singular potential with supercritical coupling I. Theory

The J-matrix method of scattering was developed to handle regular short-range potentials with applications in atomic, nuclear and molecular physics. Its accuracy, stability, and convergence properties compare favorably with other successful scattering methods. It is an algebraic method, which is built on the utilization of orthogonal polynomials that satisfy three-term recursion relations and on the manipulation of tridiagonal matrices. Recently, we extended the method to the treatment of 1/r^2 singular short-range potentials but confined ourselves to the sub-critical coupling regime where the coupling parameter strength of the 1/r^2 singularity is greater than -1/8. In this work, we expand our study to include the supercritical coupling in which the coupling parameter strength is less than -1/8. However, to accomplish that we had to extend the formulation of the method to objects that satisfy five-term recursion relations and matrices that are penta-diagonal. It is remarkable that we could develop the theory without regularization or self-adjoint extension, which are normally needed in the treatment of such highly singular potentials. Nonetheless, we had to pay the price by extending the formulation of the method into this larger representation and by coping with slower than usual convergence. In a follow-up study, we intend to apply the method to obtain scattering information for realistic potential models.

quant-ph↗

arXiv2020

Density of States Analysis of Electrostatic Confinement in Gapped Graphene

We investigate the electrostatic confinement of charge carriers in a gapped graphene quantum dot in the presence of a magnetic flux. The circular quantum dot is defined by an electrostatic gate potential delimited in an infinite graphene sheet which is then connected to a two terminal setup. Considering different regions composing our system, we explicitly determine the solutions of the energy spectrum in terms of Hankel functions. Using the scattering matrix together with the asymptotic behavior of the Hankel functions for large arguments, we calculate the density of states and show that it has an oscillatory behavior with the appearance of resonant peaks. It is found that the energy gap can controls the amplitude and width of these resonances and affect their location in the density of states profile.

cond-mat.mes-hall↗

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

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

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

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↗

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↗

arXiv2017

Analytical solutions of the Dirac equation using the Tridiagonal Representation Approach: General study, limitations, and possible applications

This paper aims at extending our previous work on the solution of the one-dimensional Dirac equation using the Tridiagonal Representation Approach (TRA). In the approach, we expand the spinor wavefunction in terms of suitable square integrable basis functions that support a tridiagonal matrix representation of the wave operator. This will transform the problem from solving a system of coupled first order differential equations to solving an algebraic three-term recursion relation for the expansion coefficients of the wavefunction. In some cases, solutions to this recursion relation can be related to well-known classes of orthogonal polynomials whereas in other situations solutions represent new class of polynomials. In this work, we will discuss various solvable potentials that obey the tridiagonal representation requirement with special emphasis on simple cases with spin-symmetric and pseudospin-symmetric potential couplings. We conclude by mentioning some potential applications in graphene.

math-ph↗

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

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↗