Abstract: We investigated the effect of different stacking order of the four graphene layer system on the induced band gap when positively charged top and negatively charged back gates are applied to the system. A tight-binding approach within a self-consistent Hartree approximation is used to calculate the induced charges on the different graphene layers. We show that the electric field does not open an energy gap if the multilayer graphene system contains a trilayer part with the ABA Bernal stacking.

Abstract: Small numbers N < 5 of two-dimensional Coulomb-interacting electrons trapped in a parabolic potential placed in a perpendicular magnetic field are investigated. The reduced wave function of this system, which is obtained by fixing the positions of N-1 electrons, exhibits strong correlations between the electrons and the zeros. These zeros axe often called vortices. An exact-diagonalization scheme is used to obtain the wave functions and the results are compared with results obtained from the recently proposed rotating electron molecule (REM) theory. We find that the vortices gather around the fixed electrons and repel each other, which is to a much lesser extend so for the REM results.

Abstract: Merged, or giant, multi-quanta vortices (GVs) appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for vortex merger. Using Bitter decoration to visualise vortices in small Nb disks, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters/GVs well below Tc and Hc2, in contrast to well-defined shells of individual vortices found in the absence of pinning.

Abstract: We present an approximate description of the giant vortex state in a thin mesoscopic superconducting disk within the phenomenological Ginzburg-Landau approach. Analytical asymptotic expressions for the energies of the states with fixed vorticity are obtained when a small magnetic flux is accumulated in the disk. The spectrum of the lowest Landau levels of such a disk is also discussed. (C) 2001 Elsevier Science B.V. All rights reserved.

Abstract: A uniform ground-state three-dimensional Fermi gas with short-range repulsive pairwise interaction is under consideration. Its kinetic and interaction energies are calculated up to the second order of the expansion in the gas parameter. Similar to recent results for an interacting Bose gas, the quantities in question are found to depend on the pairwise interaction through two characteristic lengths: the former, a, is the s-wave scattering length, and the latter, b, is related to a by b=a-m(partial derivativea/partial derivativem), where m stands for the fermion mass. To control the results, we proceed in two independent ways. The first involves the Hellmann-Feynman theorem applied to derive the kinetic and interaction energies from the total-energy expansion in the gas parameter first found by Huang and Yang. The second way operates with in-medium pair wave functions and allows one to calculate the quantities of interest “from scratch.” The results of the present investigation, taken together with those of the recent consideration of a dilute Bose gas, make it possible to conclude that the pairwise interaction in a quantum gas has an essential and nontrivial effect on the kinetic energy, which is not the case for a classical many-particle system.

Abstract: Transport properties of a two-dimensional electron gas (2DEG) are studied in the presence of a normal magnetic field B, of a weak one-dimensional (1D) periodic potential modulation V(x) = V(0)cos(Kx), and of the Rashba spin-orbit interaction (SOI) of strength a. For V(x) = 0 the SOI mixes the up and down spin states of neighboring Landau levels into two, unequally spaced energy branches. For V(x) not equal 0 these levels broaden into bands and their bandwidths oscillate with B. The n-th level bandwidth of each series vanishes at different values of B. Relative to the ID-modulated 2DEG without SOI and one flat-band condition, there are two flat-band conditions that depend on a and the transport coefficients can change considerably. For weak a the Weiss oscillations show beating patterns while for strong a the Shubnikov-de Haas ones axe split in two.

Abstract: Two concentric two-dimensional GaAs/(Al,Ga)As nanorings in a normal magnetic field are theoretically studied. The single-band effective mass approximation is adopted for both the electron and the hole states, and the analytical solutions are given. We find that the electronic single particle states are arranged in pairs, which exhibit anticrossings and the orbital momentum transitions in the energy spectrum when magnetic field increases. Their period is essentially determined by the radius of the outer ring. The oscillator strength for interband transitions is strongly reduced close to each anticrossing. We show that an optical excitonic Aharonov-Bohm effect may occur in concentric nanorings.

Abstract: We have calculated analytically the spatial distribution of the electric field and current density, and obtained the Joule heat generation rate in a two-dimensional electron gas (2DEG) subjected to a non-homogeneous magnetic field of a 'chess' configuration. The generation of the Joule heat from the 2DEG is mainly concentrated near the singular corners of each 'chess' field and tends to zero in other corners. (C) 2002 Elsevier Science B.V. All rights reserved.