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 ($n=\pm 1$).
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.
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.
When a single-layer graphene sheet is contacted with metallic electrodes, tunnel barriers are formed as a result of the doping of graphene by the metal in the contact region. If the Fermi energy level is modulated by a gate voltage, the phenomenon of Klein tunneling results in specific features in the conductance and noise. Here we obtain analytically exact solutions for the transmission and reflection probability amplitudes using a trapezoidal potential barrier, allowing us to calculate the differential conductance and the Fano factor for a graphene sheet in the ballistic regime. We put in ev…
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.
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.
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 triangu…
We solve the Dirac equation in three regions of graphene to get the solutions of the energy spectrum in connection to the strain, energy gap, and magnetic field. The Goos-Hänchen shifts and group delay time will be obtained by applying the stationary phase approximation after the wave functions at the interfaces have been matched. Our results suggest that the group delay time is influenced by the presence of strain along the armchair and zigzag directions. We show that the gate voltage and strain have the ability to change the group delay from subluminality to superluminality. This may have si…
We study the tunneling time of Dirac fermions in graphene magnetic barrier through an electrostatic potential and a mass term. This latter generates an energy gap in the spectrum and therefore affects the proprieties of tunneling of the system. For clarification, we first start by deriving the eigenspinors solutions of Dirac equation and second connect them to the incident, reflected and transmitted beam waves. This connection allows us to obtain the corresponding phases shifts and consequently compute the group delay time in transmission and reflection. Our numerical results show that the gro…
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.
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.
Van der Waal's heterostrucutures allow for novel devices such as two-dimensional-to-two-dimensional tunnel devices, exemplified by interlayer tunnel FETs. These devices employ channel/tunnel-barrier/channel geometries. However, during layer-by-layer exfoliation of these multi-layer materials, rotational misalignment is the norm and may substantially affect device characteristics. In this work, by using density functional theory methods, we consider a reduction in tunneling due to weakened coupling across the rotationally misaligned interface between the channel layers and the tunnel barrier. A…
Quantum transport in gapped graphene under strain and laser--electrostatic barriers
Laboratory of Theoretical Physics, Faculty of Sciences, Chouaïb Doukkali University（舒瓦伊布杜卡利大学理学院理论物理实验室）；Vicerrectoría de Investigación y Postgrado, Universidad de La Serena（拉塞雷纳大学研究与研究生院）；Instituto de Alta Investigación, Universidad de Tarapacá（塔拉帕卡大学高等研究院）
We investigate spin-dependent transmission in a curved graphene superlattice of $N$ cells where each one is made up of four regions. The first is concave, and the third is convex, two arcs of circles separated by a distance $d$ from flat graphene sheets. The tunneling analysis allows us to determine all transmission and reflection channels associated with our system. As a result, we show that the number of cells acts by decreasing the transmissions with the same spin. We predict a solid spin-filtering effect when $d$ and $N$ are sufficiently large. Finally, it is determined that the degree and…
Transmission profiles in bilayer graphene have been studied theoretically in presence of a pair of delta function magnetic barriers. Two types of asymmetric Fano resonances are discussed in connection to the electronic cloaking effect in graphene nanostructures. One arises in a static (time independent) vector barrier due to the quantum interference between the discrete hole like state inside the barrier and the electron like continuum outside. In this case the computed results for normal incidence indirectly verify that the cloaking effect is a manifestation of the chirality conservation in c…
We investigate the strain effect along armchair and zigzag directions on the tunneling transport of Dirac fermions in graphene laser barrier through a time dependent potential along y-axis. Our system is composed of three regions and the central one is subjected to a deformation of strength S. Based on Dirac equation and the Floquet approach, we determine the eigenvalues and eigenspinors for each region. Using the boundary conditions at interfaces together with the transfer matrix method we identify the transmission in the different Floquet sideband states as function of the physical parameter…
The group delay time of Dirac fermions subjected to a tilting barrier potential along the $ x $-axis is investigated in graphene. We start by finding the eigenspinor solution of the Dirac equation and then relating it to incident, reflected, and transmitted beam waves. This relationship allows us to compute the group delay time in transmission and reflection by obtaining the corresponding phase shifts. We discovered that the barrier width, incident energy, and incident angle can all be used to modify the group delay time, and that the particles travel through the barrier at the Fermi velocity …
Graphene electrons feature a pair of massless Dirac cones of opposite pseudospin chirality at two valleys. Klein tunneling refers to the intriguing capability of these chiral electrons to penetrate through high and wide potential barrier. The two valleys have been treated independently in the literature, where time reversal symmetry dictates that neither the normal incidence transmission nor the angle-averaged one can have any valley polarization. Here we show that, when intervalley scattering by barrier is accounted, graphene electrons normally incident at a superlattice barrier can experienc…
We have utilized the finite-difference approach to explore electron-tunneling properties in gapped graphene through various electrostatic-potential barriers changing from Gaussian to a triangular envelope function in comparison with a square potential barrier. Transmission coefficient is calculated numerically for each case and applied to corresponding tunneling conductance. It is well known that Klein tunneling in graphene will be greatly reduced in a gapped graphene. Our results further demonstrate that such a decrease of transmission can be significantly enhanced for spatially-modulated pot…
We investigate the scattering of a wave packet describing low-energy electrons in graphene by a time-dependent finite step potential barrier. Our results demonstrate that, after Klein tunneling through the barrier, the electron acquires an extra energy which depends on the rate of change the barrier height in time. If such a rate is negative, the electron loses energy and ends up as a valence band state after leaving the barrier, which effectively behaves as a positively charged quasi-particle
We investigate theoretically the transmission of electrons through a pair of δ- function magnetic barriers in graphene in presence of external monochromatic, linearly polarised and CW laser field. The transmission coefficients are calculated in the framework of non-perturbative Floquet theory using the transfer matrix method. It is noted that the usual Fabry-Perot oscillations in transmission through the graphene magnetic barriers with larger inter barrier separation takes the shape of beating oscillations in presence of the external laser field. The laser assisted transmission spectra are als…
The kinetic transport of electrons through graphene magnetic barriers is studied theoretically in presence of an external time harmonic scalar potential. The transmission coefficients are calculated in the framework of the non-perturbative Floquet theory using transfer matrix method. The time dependent scalar potential is found to suppress the usual Fabry-Perot oscillations occurring in the transmission through a constant vector potential barrier (corresponding to two oppositely directed delta-function magnetic barriers). Two types of asymmetric Fano resonances (FR) are noted and are discussed…
