Abstract: We investigate the properties of carriers in graphene-based quantum wires created by potential barriers, by means of analytical and numerical calculations. We obtain expressions for the energy spectrum as a function of barrier height, well width and linear momentum along the wire. The results demonstrate a direction-dependent resonant transmission across the potential well.

Abstract: The energy spectrum and density of states of graphene bilayer superlattices (SLs) are evaluated. We take into account doping and/or gating of the layers as well as tunnel coupling between them. In addition, we evaluate the transmission through such SLs and through single or double barriers. The transmission exhibits a strong dependence on the direction of the incident wave vector.

Abstract: We study ballistic electron transport through a finite chain of quantum circular rings in the presence of spin-orbit interaction (SOI) of strength alpha. The transmission and reflection coefficients for a single ring, obtained analytical lylead to the conductance for a chain of rings as a function of alpha and of the wave vector k of the incident electron. Due to destructive spin interferences the chain can be totaly opaque for certain ranges of k the width of which depends on the value of alpha. A periodic modulation of a widens up the gaps considerably and produces a nearly binary conductance output.

Abstract: We study ballistic electron transport through a finite chain of quantum circular rings in the presence of spin-orbit interaction of strength alpha. For a single ring, the transmission and reflection coefficients are obtained analytically and from them the conductance for a chain of rings as a function of alpha and of the wave vector k of the incident electron. We show that due to destructive spin interferences, the chain can be totally opaque for certain ranges of k, the width of which depends on the value of alpha. A periodic modulation of the strength alpha or of the ring radius widens the gaps considerably and produces a nearly binary conductance output. (C) 2004 American Institute of Physics.

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.

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 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: 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: Transport properties of the 2DEG are studied in the presence of a normal magnetic field B and of a weak, two-dimensional periodic potential modulation. A tight-binding treatment has shown that each Landau level splits into several subbands with exponentially small gaps between them. Assuming the latter are closed due to disorder gives analytical wave functions and simplifies the evaluation of the magnetoresistance tensor p(muv) The relative phase of the oscillations in p(xx) and p(yy) depends on the modulation strengths and periods. For short periods less than or equal to 100 nm, in addition to the Weiss oscillations, the collisional contribution to the conductivity and the corresponding resistivity contribution show prominent peaks when one flux quantum h/e passes through an integral number of unit cells in good agreement with experiments. For periods 300-400 nm long used in early experiments, these peaks occur at fields 10-25 times smaller than those of the Weiss oscillations and are not resolved. (C) 2003 Elsevier B.V. All rights reserved.