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.

Abstract: Electron transport through multiterminal rectangular arrays of quantum rings is studied in the presence of Rashba-type spin-orbit interaction (SOI) and of a perpendicular magnetic field. Using the analytic expressions for the transmission and reflection coefficients for single rings we obtain the conductance through such arrays as a function of the SOI strength, of the magnetic flux, and of the wave vector k of the incident electron. Due to destructive or constructive spin interferences caused by the SOI, the array can be totally opaque for certain ranges of k, while there are parameter values where it is completely transparent. Spin resolved transmission probabilities show nontrivial spin transformations at the outputs of the arrays. When pointlike random scattering centers are placed between the rings, the Aharonov-Bohm peaks split, and an oscillatory behavior of the conductance emerges as a function of the SOI strength.

Abstract: Ballistic transport of a two-dimensional electron gas (2DEG) in a rectangle shaped wire, subjected to a local nonhomogeneous magnetic field that results from an in-plane magnetized ferromagnetic (FM) strip deposited above the 2DEG, is investigated theoretically. We found a positive magnetoresistance (MR), which exhibits hysteresis behavior with respect to the direction of the magnetic field sweep, in agreement with a recent experiment. This positive MR can be tuned by applying a gate voltage to the FM strip.

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 numerically investigate the spin-orbit (SO) coupling effect on the magnetic flux evolution of energy and supercurrent in mesoscopic d-wave superconducting loops by solving the spin-generalized Bogoliubov-de Gennes equations self-consistently. It is found that the energy spectrum splits when the SO interaction is involved and the Majorana zero mode can be realized in the [100] edges of square systems for an appropriate SO coupling strength. Superconducting phase transitions appear when the energy gap closes, accompanied by energy jumps between different energy parabolas in the ground state, which provides a possible mechanism to support fractional flux periodicity of supercurrent. Moreover, in the case of rectangular loops with SO coupling, the jumps of the ground-state energy gradually disappear by increasing the ratio of length to height of the sample, and a paramagnetic response with opposite direction of the screening current around zero flux value can occur in such systems.

Abstract: A pair of electrons in vertically stacked self-assembled quantum dots is studied and the singlettriplet energy splitting is calculated in an external electric field using the configuration-interaction method. We show that for double quantum dots the dependence of the singlet energy levels on the electric field involves multiple avoided crossings of three energy levels. The exchange interaction, i.e., the energy difference of the lowest triplet and lowest singlet states, can be tuned by an electric field in a wide range of several tens of meV. For electric fields exceeding a threshold value the exchange interaction becomes a linear function of the field when the two electrons in the singlet state start to occupy the same dot. We also consider non-symmetric confinement, non-perfectly aligned dots, in horizontal as well as vertical field orientation. In a stack of three vertically coupled dots the depth of the confinement in the central dot can be used to enhance the exchange interaction. For a deeper central dot the dependence of the exchange interaction on the electric field is anomalousit initially decreases when the field is applied in both directions parallel and antiparallel to the axis of the stack. Such a behavior is never observed for a pair of quantum dots.