The energy spectrum of a graphene sheet subject to a single barrier potential having a time periodic oscillating height and subject to a magnetic field is analyzed. The corresponding transmission is studied as function of the incident energy and potential parameters. Quantum interference within the oscillating barrier has an important effect on quasiparticles tunneling. In particular the timeperiodic electrostatic potential generates additional sidebands at energies ǫ + l ω (l = 0, ±1, · · · ) in the transmission probability originating from the photon absorption or emission within the oscillating barrier. Due to numerical difficulties in truncating the resulting coupled channel equations we limited ourselves to low quantum channels, i.e. l = 0, ±1.

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

Klein tunneling and conductance for Dirac fermions in ABC-stacked trilayer graphene through symmetric and asymmetric double potential barrier are investigated. This was done by using the continuum model of two and six-bands. The numerical results show that the transport is sensitive to the height, the width, and the distance between the two barriers. It is found that the Klein paradox at normal incidence (k y = 0) and resonant features at k y ≠ 0 in the transmission result from resonant electron states in the wells or hole states in the barriers. It is shown that such features strongly influence the ballistic conductance of the structures. IntroductionGenerally, graphene [1][2][3][4] is a 2D lattice of carbon atoms arranged in hexagonal geometry. Its stacking can be realized in different methods to engineer multi-layered graphene showing various physical properties. Typical examples of stacking includes order, Bernal (AB), and rhombohedral stacking (ABC). [5][6][7][8][9][10] In the first all carbon atoms of each layer are well-aligned, while the second and third have cycle periods composed, respectively, of two and three layers of non-aligned graphene. It was shown that the band structure, Klein tunneling, band gap, transport and optical properties of graphene depend on the way how its layers are stacked [5,9,[11][12][13][14][15][16][17][18][19][20][21][22] and the applied external sources. [5,9,19,[23][24][25][26][27][28][29][30][31][32][33] Recently, trilayer graphene (TLG) has attracted more attention. [15,19,26,29,31,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49] It has two distinct allotropes: the Bernal (ABA) and rhombohedral (ABC) stackings. ABA has atoms of the top layer lie exactly on top of the bottom layer. It possess a dispersion relation as summation of the linear and quadratic dispersions corresponding to the single layer and bilayer, respectively. It has no opening gap under applied external electric field. [50] As for ABC, the atoms of one of the sublattices of topmost layer lie above the center of the hexagons of bottom layer.

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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, ±1, and study the three corresponding transmission probabilities.