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: Electrical transport properties of a two-dimensional electron gas axe studied in the presence of a perpendicular magnetic field B modulated weakly and periodically along one direction, B = (B + B0 cos Kx)z, with B0 much less than B, K = 2pi/a, and a being the period of the modulation. B0 is taken constant or proportional to B. The Landau levels broaden into bands and their width, proportional to the modulation strength B0, oscillates with B and gives rise to oscillations in the magnetoresistance at low B. These oscillations reflect the commensurability between the cyclotron diameter at the Fermi level and the period a and consequently hey are distinctly different from the Shubnikov-de Ha.as ones, at higher B, in period and temperature dependence. The bandwidth at the Fermi energy can be one order of magnitude larger, at low B, than that of the electric case for equal modulation strengths. The resulting magnetoresistance oscillations have a much higher amplitude than those of the electric case with which they are out of phase. Explicit asymptotic expressions are derived for the temperature dependence of the transport coefficients. The case when both electric and magnetic modulations are present is also considered. The position of the resulting oscillations depends on the ratio delta between the two modulation strengths. When the modulations are out of phase there is no shift in the position of the oscillations when delta varies and for a particular value of delta the oscillations are suppressed.

Abstract: The electronic properties of the two-dimensional material silicene are strongly influenced by the application of a perpendicular electric field E-z and of an exchange field M due to adatoms positioned on the surface or a ferromagnetic substrate. Within the random phase approximation, we investigate how electron-electron interactions are affected by these fields and present analytical and numerical results for the dispersion of plasmons, their lifetime, and their oscillator strength. We find that the combination of the fields E-z and M brings a spin and valley texture to the particle-hole excitation spectrum and allows the formation of spin-and valley-polarized plasmons. When the Fermi level lies in the gap of one spin in one valley, the intraband region of the corresponding spectrum disappears. For zero E-z and finite M the spin symmetry is broken and spin polarization is possible. The lifetime and oscillator strength of the plasmons are shown to depend strongly on the number of spin and valley type electrons that form the electron-hole pairs.

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: We present a theoretical study of the optoelectronic properties of monolayer graphene. Including the effect of the electron-photon-phonon scattering, we employ the mass- and energy-balance equations derived from the Boltzmann equation to evaluate self-consistently the carrier densities, optical conductance and transmission coefficient in graphene in the presence of linearly polarized radiation field. We find that the photo-excited carrier density can be increased under infrared radiation and depend strongly on radiation intensity and frequency. For short wavelengths (lambda <3 mu m), the universal optical conductance sigma(0) = e(2)/4h is obtained and the light transmittance is about 0.97-0.98. Interestingly, there is an optical absorption window in the range 4-100 mu m which is induced by different transition energies required for inter- and intra-band optical absorption. The position and width of this absorption window depend sensitively on temperature and carrier density of the system. These results are relevant for applications of recently developed graphene devices in advanced optoelectronics such as the infrared photodetectors. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

Abstract: Electrical transport properties of the two-dimensional electron gas are studied in the presence of a perpendicular magnetic field B = Bz and of a weak one-dimensional electric (V0 cos (Kx)) or magnetic (B0 = B0 cos (Kx)z) modulation where B0 << B, K = 2-pi/a, and a is the modulation period. In either case the discrete Landau levels broaden into bands whose width: (1) is proportional to the modulation strength, (2) it oscillates with B, and (3) it gives rise to magnetoresistance oscillations, at low B, that are different in period and temperature dependence from the Shubnikov-de Haas (SdH) ones, at higher B. For equal energy modulation strengths, V0 = heB0/m*, the magnetic bandwidth at the Fermi energy is about one order of magnitude larger than the electric one. The same holds for the oscillation amplitude of the electrical magnetoresistivity tensor. For two-dimensional modulations the energy spectrum has the same structure but with different scales. For weak magnetic fields and equal modulation strengths the gaps in the spectrum can be much larger in the magnetic case thus making easier the observability of the spectrum's fine structure.

Abstract: We review the energy spectrum and transport properties of several types of one-dimensional superlattices (SLs) on single-layer and bilayer graphene. In single-layer graphene, for certain SL parameters an electron beam incident on an SL is highly collimated. On the other hand, there are extra Dirac points generated for other SL parameters. Using rectangular barriers allows us to find analytical expressions for the location of new Dirac points in the spectrum and for the renormalization of the electron velocities. The influence of these extra Dirac points on the conductivity is investigated. In the limit of δ-function barriers, the transmission T through and conductance G of a finite number of barriers as well as the energy spectra of SLs are periodic functions of the dimensionless strength P of the barriers, Graphic, with vF the Fermi velocity. For a KronigPenney SL with alternating sign of the height of the barriers, the Dirac point becomes a Dirac line for P = π/2+nπ with n an integer. In bilayer graphene, with an appropriate bias applied to the barriers and wells, we show that several new types of SLs are produced and two of them are similar to type I and type II semiconductor SLs. Similar to single-layer graphene SLs, extra Dirac points are found in bilayer graphene SLs. Non-ballistic transport is also considered.

Abstract: We consider a one-dimensional (1D) superlattice (SL) on graphene consisting of very high and very thin (δ-function) magnetic and potential barriers with zero average potential and zero magnetic field. We calculate the energy spectrum analytically, study it in different limiting cases, and determine the condition under which an electron beam incident on an SL is highly collimated along its direction. In the absence of the magnetic SL the collimation is very sensitive to the value of W/Ws and is optimal for W/Ws = 1, where W is the distance between the positive and negative barriers and L = W + Ws is the size of the unit cell. In the presence of only the magnetic SL the collimation decreases and the symmetry of the spectrum around ky is broken for W/W_s\neq 1 . In addition, a gap opens which depends on the strength of the magnetic field. We also investigate the effect of spatially separated potential and magnetic δ-function barriers and predict a better collimation in specific cases.

Abstract: Ballistic electron transport through a finite chain of quantum circular rings is studied in the presence of the Rashba coupling, of strength a, and of a perpendicular magnetic field B. The transmission and reflection coefficients for a single ring, obtained analytically, help obtain the conductance through a chain of rings as a function of the strength a, the field B, and of the wave vector k of the incident electron. Due to destructive spin interferences caused by the Rashba coupling the chain can be totally opaque for certain ranges of k the width of which depends on values of a and B. Outside these ranges the conductance oscillates with high values between e(2)/h and 2e(2)/h. The effect of a periodic modulation of a or B on the conductance gaps is investigated. A periodic, square-wave conductance pattern, pertinent to the development of the spin transistor, results within wide stripes in the parameter space spanned by k, a, and B. Finite temperatures smoothen the square-wave profile of the conductance but do not alter its periodic character.

Abstract: We show how snake-orbit states which run along a magnetic edge can be confined electrically. We consider a two-dimensional electron gas (2DEG) confined into a quantum wire, subjected to a strong perpendicular and steplike magnetic field B/ − B. Close to this magnetic step, new, spatially confined bound states arise as a result of the lateral confinement and the magnetic-field step. The number of states, with energy below the first Landau level, increases as B becomes stronger or as the wire width becomes larger. These bound states can be understood as an interference between two counter-propagating one-dimensional snake-orbit states.