Abstract: A procedure to derive the Ginzburg-Landau (GL) theory from the multiband BCS Hamiltonian is developed in a general case with an arbitrary number of bands and arbitrary interaction matrix. It combines the standard Gor'kov truncation and a subsequent reconstruction in order to match accuracies of the obtained terms. This reconstruction recovers the phenomenological GL theory as obtained from the Landau model of phase transitions but offers explicit microscopic expressions for the relevant parameters. Detailed calculations are presented for a three-band system treated as a prototype multiband superconductor. It is demonstrated that the symmetry in the coupling matrix may lead to the chiral ground state with the phase frustration, typical for systems with broken time-reversal symmetry. DOI: 10.1103/PhysRevB.87.134510

Abstract: We study Dirac plasmons and their damping in spatially separated N-layer graphene structures at finite doping and temperatures. The plasmon spectrum consists of one optical excitation with square-root dispersion and N – 1 acoustical excitations with linear dispersion, which are undamped at zero temperature and finite doping within a triangular energy region outside the electron-hole continuum. In the long-wavelength limit the energy and weight of the optical plasmon modes increase, respectively, as the square root and linearly with N in agreement with recent experimental findings. The energy and weight of the upper-lying acoustical branches also increase with N. This increase is strongest for the uppermost acoustical mode, and we find that its energy can exceed at some value of momentum the plasmon energy in an individual graphene sheet. Meanwhile, the energy of the low-lying acoustical branches decreases weakly with N as compared with the single acoustical mode in double-layer graphene structures. Our numerical calculations provide a detailed understanding of the overall behavior of the wave-vector dependence of the optical and acoustical multilayer plasmon modes and show how their dispersion and damping are modified as a function of temperature, interlayer spacing, and inlayer carrier density in (un)balanced graphene multilayer structures. DOI: 10.1103/PhysRevB.87.085401

Abstract: We investigate the influence of an external perpendicular magnetic field on the lowest-energy states of an electron bound to a donor which is located near a semiconductor-metal interface. The problem is treated within the effective mass approach and the lowest-energy states are obtained through (1) the “numerically exact” finite element method, and (2) a variational approach using a trial wave function where all image charges that emerge due to the presence of the metallic gate are taken into account. The trial wave functions are constructed such that they reduce to an exponential behavior for sufficiently small magnetic fields and become Gaussian for intermediate and large magnetic fields. The average electron-donor distance can be controlled by the external magnetic field. We find that the size of the 2p(z) state depends strongly on the magnetic field when the donor is close to the interface, showing a nonmonotonic behavior, in contrast with the ground and the other excited states. DOI: 10.1103/PhysRevB.87.075313

Abstract: Themean-field Hubbard model is used to investigate the formation of the antiferromagnetic phase in hexagonal graphene rings with inner zigzag edges. The outer edge of the ring was taken to be either zigzag or armchair, and we found that both types of structures can have a larger antiferromagnetic interaction as compared with hexagonal dots. This difference could be partially ascribed to the larger number of zigzag edges per unit area in rings than in dots. Furthermore, edge states localized on the inner ring edge are found to hybridize differently than the edge states of dots, which results in important differences in the magnetism of graphene rings and dots. The largest staggered magnetization is found when the outer edge has a zigzag shape. However, narrow rings with armchair outer edge are found to have larger staggered magnetization than zigzag hexagons. The edge defects are shown to have the least effect on magnetization when the outer ring edge is armchair shaped. DOI: 10.1103/PhysRevB.87.085434

Abstract: We study the mobility of Dirac fermions in monolayer graphene on a GaAs substrate, limited by the combined action of the extrinsic potential of piezoelectric surface acoustical phonons of GaAs (PA) and of the intrinsic deformation potential of acoustical phonons in graphene (DA). In the high-temperature (T) regime, the momentum relaxation rate exhibits the same linear dependence on T but different dependencies on the carrier density n, corresponding to the mobility mu proportional to 1 root n and 1/n, respectively for the PA and DA scattering mechanisms. In the low-T Bloch-Gruneisen regime, the mobility shows the same square-root density dependence mu proportional to root n, but different temperature dependencies mu proportional to T-3 and T-4, respectively for PA and DA phonon scattering. DOI: 10.1103/PhysRevB.87.075443

Abstract: The Green function approach to the Bardeen-Cooper-Schrieffer theory of superconductivity is used to study nanofilms. We go beyond previous models and include effects of confinement on the strength of the electron-phonon coupling as well as on the electronic spectrum and on the phonon modes. Within our approach, we find that in ultrathin films, confinement effects on the electronic screening become very important. Indeed, contrary to what has been advanced in recent years, the sudden increases of the density of states when new bands start to be occupied as the film thickness increases, tend to suppress the critical temperature rather than to enhance it. On the other hand, the increase of the number of phonon modes with increasing number of monolayers in the film leads to an increase in the critical temperature. As a consequence, the superconducting critical parameters in such nanofilms are determined by these two competing effects. Furthermore, in sufficiently thin films, the condensate consists of well-defined subcondensates associated with the occupied bands, each with a distinct coherence length. The subcondensates can interfere constructively or destructively giving rise to an interference pattern in the Cooper pair probability density.

Abstract: The interaction of an injected electron towards a quantum dot (QD) containing a single confined electron is investigated using a flexible time-dependent quantum mechanics formalism, which allows both electrons to move and undergo quantum transitions. Different scenarios combining quantum dot dimensions, dielectric constant, injected wave packet energy, and width were explored, and our main results are: (i) due to the large characteristic transitions times between the confined state in the quantum dot and the delocalized state in the continuum, it is relatively difficult to ionize the occupied QD by Coulomb interaction solely and (ii) the charging state of the quantum dot can be sensed by direct injection of charges. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4759292]

Abstract: Within the time-dependent Ginzburg-Landau theory we study the dynamic properties of current-carrying superconducting strips in the presence of a perpendicular magnetic field. We found pronounced voltage peaks as a function of the magnetic field, the amplitude of which depends both on sample dimensions and external parameters. These voltage oscillations are a consequence of moving vortices, which undergo alternating static and dynamic phases. At higher fields or for high currents, the continuous motion of vortices is responsible for the monotonic background on which the resistance oscillations due to the entry of additional vortices are superimposed. Mechanisms for such vortex-assisted resistance oscillations are discussed. Qualitative changes in the magnetoresistance curves are observed in the presence of random defects, which affect the dynamics of vortices in the system.

Abstract: Using the Ginzburg-Landau (GL) theory, we calculate the stability of sample symmetry-induced vortex-antivortex molecules in a mesoscopic superconducting bilayer exposed to a homogeneous magnetic field. We demonstrate the conditions under which the two condensates cooperatively broaden the field-temperature stability range of the composite (joint) vortex-antivortex state. In cases when such broadening is not achieved, a reentrance of the vortex-antivortex state is found at lower temperatures. In a large portion of the phase diagram noncomposite states are possible, in which the antivortex is present in only one of the layers. In this case, we demonstrate that the vortex-antivortex molecule in one of the layers can be pinned and enlarged by interaction with a vortex molecule in the other. Using analogies in the respective GL formalisms, we map our findings for the bilayer onto mesoscopic two-band superconductors.

Abstract: The current voltage (IV) characteristics of short [with length L less than or similar to xi(T)] and long [L >> xi(T)] microbridges are theoretically investigated near the critical temperature of the superconductor. Calculations are made in the nonlocal (local) limit when the inelastic relaxation length due to electron-phonon interactions L(in) = (D tau(in))(1/2) is larger (smaller) than the temperature-dependent coherence length xi(T) (D is the diffusion coefficient, tau(in) is the inelastic relaxation time of the quasiparticle distribution function). We find that, in both limits, the origin of the hysteresis in the IV characteristics is mainly connected with the large time scale over which the magnitude of the order parameter varies in comparison with the time-scale variation of the superconducting phase difference across the microbridge in the resistive state. In the nonlocal limit, the time-averaged heating and cooling of quasiparticles are found in different areas of the microbridge, which are driven, respectively, by oscillations of the order parameter and the electric field. We show that, by introducing an additional term in the time-dependent Ginzburg-Landau equation, it is possible to take into account the cooling effect in the local limit too.

Abstract: Using highly efficient simulations of the tight-binding Bogoliubov-de-Gennes model, we solved self-consistently for the pair correlation and the Josephson current in a superconducting-bilayer graphene-superconducting Josephson junction. Different doping levels for the non-superconducting link are considered in the short- and long-junction regimes. Self-consistent results for the pair correlation and superconducting current resemble those reported previously for single-layer graphene except at the Dirac point, where remarkable differences in the proximity effect are found, as well as a suppression of the superconducting current in the long-junction regime. Inversion symmetry is broken by considering a potential difference between the layers and we found that the supercurrent can be switched if the junction length is larger than the Fermi length.

Abstract: We present a theoretical study of the electronic structure of a heavily Si delta-doped layer in a GaAs/AlxGa1-xAs/GaAs quantum barrier. In this class of structures the effect of DX centers on the electronic properties can be tuned by changing the AlxGa1-xAs barrier width and/or the Al concentration, which leads to a lowering of the DX level with respect to the Fermi energy without disturbing the wave functions much. A self-consistent approach is developed in which the effective confinement potential and the Fermi energy of the system, the energies, the wave functions, and the electron densities of the discrete subbands have been obtained as a function of both the material parameters of the samples and the experimental conditions. The effect of DX centers on such structures at nonzero temperature and under an external pressure is investigated for three different models: (1) the DX(nc)(0) model with no correlation effects, (2) the d(+)/DX(0) model, and (3) the d(+)/DX(-) model with inclusion of correlation effects. In the actual calculation, influences of the background accepters, the discontinuity of the effective mass of the electrons at the interfaces of the different materials, band nonparabolicity, and the exchange-correlation energy of the electrons have been taken into account. We have found that (1) introducing a quantum barrier into delta-doped GaAs makes it possible to control the energy gaps between different electronic; subbands; (2) the electron wave functions are mon spread out when the repellent effect of the barriers is increased as compared to those in delta-doped GaAs; (3) increasing the quantum-barrier height and/or the application of hydrostatic pressure are helpful to experimentally observe the effect of the DX centers through a decrease of the total free-electron density; and (4) the correlation effects of the charged impurities are important for the systems under study.

Abstract: Spatially nonhomogeneously spin polarized nuclei are proposed as a new mechanism to monitor electron states in a nanostructure, or as a means to create and, if necessary, reshape such nanostructures in the course of the experiment. We found that a polarization of nuclear spins may lift the spin polarization of the electron states in a nanostructure and, if sufficiently strong, leads to a polarization of the electron spins. Polarized nuclear spins may form an energy landscape capable of binding electrons with energy up to several meV and the localization radius > 100 Angstrom. (C) 2002 Elsevier Science B.V. All rights reserved.

Abstract: Explicit analytic expressions are obtained for the density of states D(E) and Fermi energy E-F of a two-dimensional electron gas in the presence of a weak and periodic unidirectional electric or magnetic modulation and of a uniform perpendicular magnetic field B. The Landau levels broaden into bands and their width, proportional to the modulation strength, oscillates with B and gives rise to Weiss oscillations in D(E), E-F and the transport coefficients. When both electric and magnetic modulations are present 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: 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.