Abstract: The electron energy spectrum in monolayer-bilayer-monolayer and in bilayer-monolayer-bilayer graphene structures is investigated and the effects of a perpendicular magnetic field and electric bias are studied. Different types of monolayer-bilayer interfaces are considered as zigzag (ZZ) or armchair (AC) junctions which modify considerably the bulk Landau levels (LLs) when the spectra are plotted as a function of the center coordinate of the cyclotron orbit. Far away from the two interfaces, one obtains the well-known LLs for extended monolayer or bilayer graphene. The LL structure changes significantly at the two interfaces or junctions where the valley degeneracy is lifted for both types of junctions, especially when the distance between them is approximately equal to the magnetic length. Varying the nonuniform bias and the width of this junction-to-junction region in either structure strongly influence the resulting spectra. Significant differences exist between ZZ and AC junctions in both structures. The densities of states (DOSs) for unbiased structures are symmetric in energy whereas those for biased structures are asymmetric. An external bias creates interface LLs in the gaps between the LLs of the unbiased system in which the DOS can be quite small. Such a pattern of LLs can be probed by scanning tunneling microscopy.

Abstract: We investigate the energy levels and optical properties of a circular graphene quantum dot in the presence of an external magnetic field perpendicular to the dot. Based on the Dirac-Weyl equation and assuming zero outward current at the edge of the dot we present the results for two different types of boundary conditions, i.e. infinite-mass (IMBC) and zigzag boundary conditions. We found that the dot with zigzag edges displays a zero-energy state in the energy spectra while this is not the case for the IMBCs. For both boundary conditions, the confinement becomes dominated by the magnetic field, where the energy levels converge to the Landau levels as the magnetic field increases. The effect of boundary conditions on the electron-and hole-energy states is found to affect the interband absorption spectra, where we found larger absorption in the case of IMBCs. The selection rules for interband optical transitions are determined and discussed for both boundary conditions.

Abstract: We investigate the effect of an external magnetic field on the carrier states that are localized at a potential kink and a kink-antikink in bilayer graphene. These chiral states are localized at the interface between two potential regions with opposite signs.

Abstract: Using the tight-binding approach coupled with mean-field Hubbard model, we theoretically study the effect of mechanical deformations on the magnetic properties of bilayer graphene (BLG) quantum dots (QDs). Results are obtained for AA-and AB(Bernal)-stacked BLG QDs, considering different geometries (hexagonal, triangular and square shapes) and edge types (armchair and zigzag edges). In the absence of strain, our results show that (i) the magnetization is affected by taking different dot sizes only for hexagonal BLG QDs with zigzag edges, exhibiting different critical Hubbard interactions, and (ii) the magnetization does not depend on the interlayer hopping energies, except for the geometries with zigzag edges and AA stacking. In the presence of in-plane and uniaxial strain, for all geometries we obtain two different magnetization regimes depending on the applied strain amplitude. The appearance of such different regimes is due to the breaking of layer and sublattice symmetries in BLG QDs.

Abstract: The conduction electrons in graphene promise new opportunities to access the region of strong many-body electron-electron correlations. Extremely high quality, atomically flat two-dimensional electron sheets and quasi-one-dimensional electron nanoribbons with tuneable band gaps that can be switched on by gates, should exhibit new many-body phenomena that have long been predicted for the regions of phase space where the average Coulomb repulsions between electrons dominate over their Fermi energies. In electron nanoribbons a few nanometres wide etched in monolayers of graphene, the quantum size effects and the van Hove singularities in their density of states further act to enhance electron correlations. For graphene multilayers or nanoribbons in a double unit electron-hole geometry, it is possible for the many-body electron-hole correlations to be made strong enough to stabilise high-temperature electron- hole superfluidity.

Abstract: The spectrum of a Coulomb impurity in bilayer graphene is investigated as function of the strength of a perpendicular magnetic field for different values of the angular quantum number m and for different values of the gate voltage. We point out fundamental differences between the results from the two-band and four-band model. The supercritical instability and fall-to-center phenomena are investigated in the presence of a magnetic field. We find that in the four-band model the fall-to-center phenomenon occurs as in monolayer graphene, while this is not the case in the two-band model. We find that in a magnetic field the supercritical instability manifests itself as a series of anticrossings in the hole part of the spectrum for states coming from the low-energy band. However, we also find very distinct anticrossings in the electron part of the spectrum that continue into the hole part, which are related to the higher energy band of the four-band model. At these anticrossings, we find a very sharp peak in the probability density close to the impurity, reminiscent for the fall-to-center phenomenon. In this paper, these peculiar and interesting effects are studied for different magnetic field, interlayer coupling, and bias potential strengths.

Abstract: The effect of the magnetic impurities on the charge transport in a magnetic topological ultra-thin film (MTF) is analytically investigated by applying the semi-classical Boltzmann framework through a modified relaxation-time approximation. Our results for the relaxation time of electrons as well as the charge conductivity of the system exhibit two distinct regimes of transport. We show that the generated charge current in a MTF is always dissipative and anisotropic when both conduction bands are involved in the charge transport. The magnetic impurities induce a chirality selection rule for the transitions of electrons which can be altered by changing the orientation of the magnetic impurities. On the other hand, when a single conduction band participates in the charge transport, the resistivity is isotropic and can be entirely suppressed due to the corresponding chirality selection rule. Our findings propose a method to determine an onset thickness at which a crossover from a three-dimensional magnetic topological insulator to a (two-dimensional) MTF occurs.

Abstract: We study the effect of structural inversion asymmetry, induced by the presence of substrates or by external electric fields, on charge transport in magnetic topological ultra-thin films. We consider general orientations of the magnetic impurities. Our results are based on the Boltzmann formalism along with a modified relaxation time scheme. We show that the structural inversion asymmetry enhances the charge transport anisotropy induced by the magnetic impurities and when only one conduction subband contributes to the charge transport a dissipationless charge current is accessible. We demonstrate how a substrate or gate voltage can control the effect of the magnetic impurities on the charge transport, and how this depends on the orientation of the magnetic impurities.

Abstract: The possibility of an inhomogeneous charge density wave phase is investigated in a system of two coupled electron and hole monolayers separated by a hexagonal boron nitride insulating layer. The charge-density-wave state is induced through the assumption of negative compressibility of electron/hole gases in a Coulomb drag configuration between the electron and hole sheets. Under equilibrium conditions, we derive analytical expressions for the density oscillation along the zigzag and armchair directions. We find that the density modulation not only depends on the sign of the compressibility but also on the anisotropy of the low-energy bands. Our results are applicable to any two-dimensional system with anisotropic parabolic bands, characterized by different effective masses. For equal effective masses, i.e., isotropic energy bands, our results agree with Hroblak et al. [Phys. Rev. B 96, 075422 (2017)]. Our numerical results are applied to phosphorene.