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.

Electron transport through a one-dimensional ring connected with two external leads, in the presence of spin-orbit interaction (SOI) of strength α and a perpendicular magnetic field is studied. Applying Griffith's boundary conditions we derive analytic expressions for the reflection and transmission coefficients of the corresponding one-electron scattering problem. We generalize earlier conductance results by Nitta et al. [Appl. Phys. Lett. 75, 695 (1999)] and investigate the influence of α, temperature, and a weak magnetic field on the conductance. Varying α and temperature changes the position of the minima and maxima of the magnetic-field dependent conductance, and it may even convert a maximum into a minimum and vice versa. 71.70.Ej, 03.65.Vf, Recently, much attention has been paid to the manipulation of the spin degrees of freedom of conduction charges in low-dimensional semiconductor structures. An important feature of the electron transport in multiply connected systems is that the conductance shows signatures of quantum interference that depend on the electromagnetic potentials:Aharonov-Bohm and Aharonov-Casher effect [1,2,3,4,5,6,7,8,9,10]. A comprehensive review of results for metallic rings is given in Ref. [11]. Many devices have been proposed to utilize additional topological phases acquired by the electrons travelling through quantum circuits [1,12,13,14,15]. Nitta et. al. proposed a spin-interference device [1] allowing considerable modulation of the electric current. This device is a one-dimensional ring connected with two external leads, made of a semiconductor structure in which the Rashba spin-orbit interaction (SOI) [16] is the dominant spin-splitting mechanism. The key idea was that, even in the absence of an external magnetic field, the difference in the Aharonov-Casher phase [3,6] acquired between carriers, travelling clockwise and counterclockwise, would produce interference effects in the spin-sensitive electron transport. By tuning the strength α of the SOI the phase difference could be changed, hence the conductance could be modulated.Nitta et. al. [1] found that the conductance G is given approximatively by

We investigate the influence of a periodic weak modulation along the x direction on the electrical and thermal properties of a two-dimensional electron gas in the presence of a perpendicular magnetic field. The modulation lifts the degeneracy of the Landau levels and leads to one-dimensional magnetic bands whose bandwidth oscillates as a function of the magnetic field. At weak magnetic fields this gives rise to the Weiss oscillations in the magnetoresistance, discovered recently, which have a very weakly temperature-dependent amplitude and a period proportional to Qn"when n, is the electron density.Diffusion-current contributions, proportional to the square of the bandwidth, dominate p"", and collisional contributions, varying approximately as the square of the density of states, dominate p» The result is that p""and p» oscillate out of phase as observed. Asymptotic analytical expressions are presented for the conductivity tensor. Similar oscillations, of much smaller amplitude, occur in the thermodynamic quantities, such as the magnetization, the susceptibility, and the specific heat. We also predict oscillations in the Ha11 resistance, the cyclotron resonance position, the linewidth, as well as in the thermal conductivity and thermopower.The components of the thermal-resistance tensor have a magnetic-field dependence similar to that of the electrical-resistivity tensor.

Near tunneling structures are proposed consisting of magnetic barriers that can be created by lithographic patterning of ferromagnetic or superconducting Slms. The form of the equivalent potential for such a barrier depends on the vive vector of the incident electron. This renders the transmission through such structures an inherently 20 process since the tunneling probability depends not only on the electron's momentum perpendicular to the tunnehng barrier but also on its momentum parallel to the barrier. Pronounced resonances are obtaitted for the tunneling probability and the conductance of a resonant tunneling device consisting of such magnetic barriers.