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: The Aharonov-Bohm (AB) effect in square phosphorene quantum rings, with armchair and zigzag edges, is investigated using the tight-binding method. The energy spectra and wave functions of such rings, obtained as a function of the magnetic flux Phi threading the ring, are strongly influenced by the ringwidthW, an in-plane electric field E-p, and a side-gating potential V-g. Compared to a square dot, the ring shows an enhanced confinement due to its inner edges and an interedge coupling along the zigzag direction, both of which strongly affect the energy spectrum and the wave functions. The energy spectrum that is gapped consists of a regular part, of conduction (valence) band states, that shows the usual AB oscillations in the higher-(lower-) energy region, and of edge states, in the gap, that exhibit no AB oscillations. As the width W decreases, the AB oscillations become more distinct and regular and their period is close to Phi(0)/2, where the flux quantum Phi(0) = h/e is the period of an ideal circular ring (W -> 0). Both the electric field E-p and the side-gating potential V-g reduce the amplitude of the AB oscillations. The amplitude can be effectively tuned by E-p or V-g and exhibits an anisotropic behavior for different field directions or side-gating configurations.

Abstract: We study transport properties of a MoS2 monolayer in the presence of a perpendicular magnetic field B. We derive and discuss its band structure and take into account spin and valley Zeeman effects. Compared to a conventional two-dimensional electron gas, these effects lead to new quantum Hall plateaus and new peaks in the longitudinal resistivity as functions of the magnetic field. The field B leads to a significant enhancement of the spin splitting in the conduction band, to a beating of the Shubnikov-de Haas (SdH) oscillations in the low-field regime, and to their splitting in the high-field regime. The Zeeman fields suppress significantly the beating of the SdH oscillations in the low-field regime and strongly enhance their splitting at high fields. The spin and valley polarizations show a similar beating pattern at low fields and are clearly separated at high fields in which they attain a value higher than 90%.

Abstract: The electronic properties of monolayer phosphorene are exotic due to its puckered structure and large intrinsic direct band gap. We derive and discuss its band structure in the presence of a perpendicular magnetic field. Further, we evaluate the magneto-optical Hall and longitudinal optical conductivities as functions of temperature, magnetic field, and Fermi energy, and show that they are strongly influenced by the magnetic field. The imaginary part of the former and the real part of the latter exhibit regular interband oscillations as functions of the frequency omega in the range (h) over bar omega similar to 1.5-2 eV. Strong intraband responses in the latter and weak ones in the former occur at much lower frequencies. The magneto-optical response can be tuned in the microwave-to-terahertz and visible frequency ranges in contrast with a conventional two-dimensional electron gas or graphene in which the response is limited to the terahertz regime. This ability to isolate carriers in an anisotropic structure may make phosphorene a promising candidate for new optical devices.

Abstract: The low-energy physics of silicene is described by Dirac fermions with a strong spin-orbit interaction and its band structure can be controlled by an external perpendicular electric field E-z. We investigate the commensurability oscillations in silicene modulated by a weak periodic potential V = V-0 cos(2 pi y/a(0)) with a(0) as its period, in the presence of a perpendicular magnetic field B and of a weak sinusoidal electric field E-z = E-0 cos(2 pi y/b(0)), where b(0) is its period. We show that the spin and valley degeneracy of the Landau levels is lifted, due to the modulation, and that the interplay between the strong spin-orbit interaction and the potential and electric field modulations can result in spin- and valley-resolved magnetotransport. At very weak magnetic fields the commensurability oscillations induced by a weak potential modulation can exhibit a beating pattern depending on the strength of the homogenous electric field Ez but this is not the case when only Ez is modulated. The Hall conductivity plateaus acquire a step structure, due to spin and valley intra-Landau-level transitions, that is absent in unmodulated silicene. The results are critically contrasted with those for graphene and the two-dimensional electron gas.

Abstract: Magnetotransport in bilayer graphene in the presence of a weak and periodic potential is investigated in the presence of a perpendicular magnetic field B. The modulation broadens the Landau levels into bands and for weak magnetic fields leads to the well-known Weiss oscillations in their bandwidth and their transport coefficients at very low B and to the Shubnikov-de Haas oscillations at larger B. The amplitude of the Weiss oscillations is severely reduced if the periodic potentials applied to the two layers oscillate out of phase. We also contrast some results with those corresponding to single-layer graphene. Relative to them the flat-band condition and the oscillation amplitude differ substantially, due to the interlayer coupling, and agree only when this coupling is extremely weak. We further show that the Hall conductivity exhibits the well-known steps at half-integer and integer multiples of 4e(2)/h in single-layer and bilayer graphene, respectively, even for very weak magnetic fields. The results are pertinent to weak and periodic corrugations when the potential modulation dominates the strain-induced magnetic modulation.

Abstract: We study in detail the optoelectronic properties of graphene. Considering the electron interactions with photons and phonons, we employ the mass- and energy-balance equations to self-consistently evaluate the photoinduced carrier densities, the optical conductance, and the transmission coefficient in the presence of a linearly polarized radiation field. We demonstrate that the photoinduced carrier densities increase around the electron-photon-phonon resonant transition. They depend strongly on the radiation intensity and frequency, temperature, and dark carrier density. For short-wavelength radiation (L<3 μm), we obtain the universal optical conductance σ0=e2/(4ℏ). Importantly, there exists an optical-absorption window in the radiation wavelength range 4100 μm, which is induced by different transition energies required for interband and intraband optical absorption. The position and width of this window depend sensitively on the temperature and the carrier density of the system. These theoretical results are in line with recent experimental findings and indicate that graphene exhibits important features not only in the visible regime but also in the midinfrared bandwidth.

Abstract: We investigate the emergence of extra Dirac points in the electronic structure of a periodically spaced barrier system, i.e., a superlattice, on single-layer graphene, using a Dirac-type Hamiltonian. Using square barriers allows us to find analytic expressions for the occurrence and location of these new Dirac points in k space and for the renormalization of the electron velocity near them in the low-energy range. In the general case of unequal barrier and well widths the new Dirac points move away from the Fermi level and for given heights of the potential barriers there is a minimum and maximum barrier width outside of which the new Dirac points disappear. The effect of these extra Dirac points on the density of states and on the conductivity is investigated.

Abstract: We investigate localized electron and hole states in parabolic quantum dots of biased graphene bilayers in the presence of a perpendicular magnetic field. These quantum dots can be created by means of nanostructured gates or by position-dependent doping, which can create a gap in the otherwise gapless dispersion of a graphene bilayer. Numerical results show the energy levels of confined electrons and holes as a function of the dot parameters and the magnetic field. Remarkable crossings of energy levels are found.

Abstract: We evaluate the transmission and conductance through magnetic barrier structures in bilayer graphene. In particular we consider a magnetic step, single and double barriers, -function barriers, as well as barrier structures that have average magnetic field equal to zero. The transmission depends strongly on the direction of the incident electron or hole wavevector and gives the possibility to construct a direction-dependent wavevector filter. The results contrast sharply with previous results on single-layer graphene. In general, the angular range of perfect transmission becomes drastically wider and the gaps narrower. This perfect transmission range decreases with the number of barriers, the barrier width, and the magnetic field. Depending on the structure, a variety of transmission resonances occur that are reflected in the conductance through the structure.