Abstract: Motivated by two-band superconductivity in, e.g., borides and pnictides, starting from the two-band Ginzburg-Landau energy functional, we discuss how the presence of two order parameters and the coupling between them influence a superconducting ring in the fluctuative regime. Our method is an extension of the von OppenRiedel formalism for rings; it is exact, but requires numerical implementation. We also study approximations for which analytic expressions can be obtained, and check their ranges of validity. We provide estimates for the temperature ranges where fluctuations are important, calculate the persistent current in MgB2 rings as a function of temperature and enclosed flux, and point out its additional dependence on the cross-section area of the wire from which the ring is made. We find temperature regions in which fluctuations enhance the persistent currents and regions where they inhibit the persistent current. The presence of two order parameters that can fluctuate independently always leads to larger averages of the order parameters at Tc, but yields larger persistent current only for appropriate parameters. In cases of very different material parameters for the two coupled condensates, the persistent current is inhibited.

Abstract: The interplay between quantum Hall states and Cooper pairs is usually hindered by the suppression of the superconducting state due to the strong magnetic fields needed to observe the quantum Hall effect. From this point of view, graphene is special since it allows the creation of strong pseudomagnetic fields due to strain. We show that in a Josephson junction made of strained graphene, Cooper pairs will diffuse into the strained region. The pair correlation function will be sublattice polarized due to the polarization of the local density of states in the zero pseudo-Landau level. We uncover two regimes: (1) one in which the cyclotron radius is larger than the junction length, in which case the supercurrent will be enhanced, and (2) the long junction regime where the supercurrent is strongly suppressed because the junction becomes an insulator. In the latter case quantized Hall states form and Andreev scattering at the normal/superconducting interface will induce edge states. Our numerical calculation has become possible due to an extension of the Chebyshev-Bogoliubovde Gennes method to computations on video cards (GPUs).

Abstract: An analytical approach, using the Dirac-Weyl equation, is implemented to obtain the energy spectrum and optical absorption of a circular graphene quantum dot in the presence of an external magnetic field. Results are obtained for the infinite-massand zigzag boundary conditions. We found that the energy spectrum of a dot with the zigzag boundary condition exhibits a zero-energy band regardless of the value of the magnetic field, while for the infinite-mass boundary condition, the zero-energy states appear only for high magnetic fields. The analytical results are compared to those obtained from the tight-binding model: (i) we show the validity range of the continuum model and (ii) we find that the continuum model with the infinite-mass boundary condition describes rather well its tight-binding analog, which can be partially attributed to the blurring of the mixed edges by the staggered potential.

Abstract: Electron transport through a spin-orbit-coupled quantum ring is investigated within linear response theory. We show that the finite width of the ring results in the appearance of Fano resonances in the conductance. This turns out to be a consequence of the spin-orbit interaction that leads to a breaking of the parity of the states localized in the ring. The resonances appear when the system is close to maxima of Aharonov-Casher conductance oscillations where spin transfer is heavily modified. When the spin-orbit coupling strength is detuned from the Aharonov-Casher maxima the resonances are broadened resulting in a dependence of the spin transport on the electron Fermi energy in contrast to predictions from one-dimensional models.

Abstract: The scattering of two-dimensional (2D) massless Dirac electrons is investigated in the presence of a random array of circular mass barriers. The inverse momentum relaxation time and the Hall factor are calculated and used to obtain parallel and perpendicular resistivity components within linear transport theory. We found a nonzero perpendicular resistivity component which has opposite sign for electrons in the different K and K′ valleys. This property can be used for valley filter purposes. The total cross section for scattering on penetrable barriers exhibits resonances due to the presence of quasibound states in the barriers that show up as sharp gaps in the cross section while for Schrödinger electrons they appear as peaks.

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 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: The structural phase transitions with electric-quadrupole long-range order in NpO2 (Fm (3) over barm-->Pn (3) over barm) and UO2 (Fm (3) over barm-->Pa (3) over bar) are analyzed from a group theoretical point of view. In both cases, the symmetry lowering involves three quadrupolar components belonging to the irreducible representation T-2g (Gamma(5)) of O-h and condensing in a triple-q structure at the X point of the Brillouin zone. The Pa (3) over bar structure is close to Pn (3) over barm, but allows for oxygen displacements. The Pa (3) over bar ordering leads to an effective electrostatic attraction between electronic quadrupoles while the Pn (3) over barm ordering results in a repulsion between them. It is concluded that the Pn (3) over barm structure can be stabilized only through some additional process such as strengthening of the chemical bonding between Np and O. We also derive the relevant structure-factor amplitudes for Pn (3) over barm and Pa (3) over bar, and the effect of domains on resonant x-ray scattering experiments.

Abstract: Applying the time-dependent Ginzburg-Landau equations, transitions between metastable states of a superconducting ring are investigated in the presence of an external magnetic field. It is shown that if the ring exhibits several metastable states at a particular magnetic field, the transition from one metastable state to another one is governed by both the relaxation time of the absolute value of the order parameter tau(\psi\) and the relaxation time of the phase of the order parameter tau(phi). We found that the larger the ratio tau(\psi\)/tau(phi), the closer the final state will be to the absolute minimum of the free energy, i.e., the thermodynamic equilibrium. The transition to the final state occurs through a subsequent set of single phase slips at a particular point along the ring.

Abstract: The magnetic coupling between two concentric mesoscopic superconductors with nonzero thickness is studied using the nonlinear Ginzburg-Landau theory. We calculated the free energy, the expelled field, the total field profile, the Cooper-pair density, and the current density distribution. By putting a smaller superconducting disk or ring in the center of a larger ring, the properties change drastically. Extra ground-state transitions are found, where the total vorticity stays the same, but the vorticity of the inner superconductor changes by 1. Due to the magnetic coupling, the current in the external ring exhibits extra jumps at the transition fields where the vorticity of the inner superconductor changes. In this case, for certain temperatures, re-entrant behavior and switching on and off of the superconducting behavior of the rings are found as a function of the magnetic field. A H-T phase diagram is obtained for the situation where the inner ring has a higher critical temperature than the outer ring. An analytic expression for the magnetic coupling is obtained for thin rings and extreme type-II superconductors.

Abstract: A polycrystalline sample of LuFe2O4 has been investigated by means of powder synchrotron x-ray and neutron diffraction and transmission electron microscopy (TEM), along with Mössbauer spectroscopy and transport and magnetic properties. A monoclinic distortion is unambiguously evidenced, and the crystal structure is refined in the monoclinic C2/m space group [aM = 5.9563(1) Å, bM = 3.4372(1) Å, cM = 8.6431(1) Å, β = 103.24(1)°]. Along with the previously reported modulations distinctive of the charge-ordering (CO) of the iron species, a new type of incommensurate order is observed, characterized by a vector q⃗1 = α1a⃗M* + γ1c⃗M* (with α1 ≅ 0.55, γ1 ≅ 0.13). In situ heating TEM observations from 300 to 773 K confirm that the satellites associated with q⃗1 vanish completely, only at a temperature significantly higher than the CO temperature. This incommensurate modulation has a displacive character and corresponds primarily to a transverse displacive modulation wave of the Lu cations position, as revealed by the high resolution, high angle annular dark field scanning TEM images and in agreement with synchrotron data refinements. Analyses of vacuum-annealed samples converge toward the hypothesis of a new ordering mechanism, associated with a tiny oxygen deviation from the O4 stoichiometry.

Abstract: The low-temperature transport properties are studied for electrons confined in delta-doped semiconductor structures with two sheets in parallel. The subband quantum mobility and transport mobility are calculated numerically for the Si delta-doped GaAs systems. The effect of coupling of the two delta layers on the electron transport is investigated. Our calculations are in good agreement with experimental results.

Abstract: Electrical transport properties of the two-dimensional electron gas are studied in the presence of a perpendicular magnetic field B = Bz and of a weak one-dimensional electric (V0 cos (Kx)) or magnetic (B0 = B0 cos (Kx)z) modulation where B0 << B, K = 2-pi/a, and a is the modulation period. In either case the discrete Landau levels broaden into bands whose width: (1) is proportional to the modulation strength, (2) it oscillates with B, and (3) it gives rise to magnetoresistance oscillations, at low B, that are different in period and temperature dependence from the Shubnikov-de Haas (SdH) ones, at higher B. For equal energy modulation strengths, V0 = heB0/m*, the magnetic bandwidth at the Fermi energy is about one order of magnitude larger than the electric one. The same holds for the oscillation amplitude of the electrical magnetoresistivity tensor. For two-dimensional modulations the energy spectrum has the same structure but with different scales. For weak magnetic fields and equal modulation strengths the gaps in the spectrum can be much larger in the magnetic case thus making easier the observability of the spectrum's fine structure.

Abstract: The density of states (DOS) and the optical conductivity of graphene is calculated in the presence of a perpendicular magnetic field and where scattering on charged and short-range impurities is included. The standard Kubo formula is employed where the self-energy induced by impurity scattering and the Green's function are calculated self-consistently including inter-Landau level (LL) coupling and screening effects. It is found that the scattering from those two types of impurities results in a symmetric LL broadening and asymmetric inter-LL coupling renormalizes the LL positions to lower energy. The peak position and intensity of the magneto-optical conductivity depends on the filling factor and the broadened DOS. Good agreement is found with recent cyclotron resonance measurements.

Abstract: We study the effect of electron confinement on the superconducting-to-normal phase transition driven by a magnetic field and/or on the current-carrying state of the superconducting condensate in nanowires. Our investigation is based on a self-consistent numerical solution of the Bogoliubov-de Gennes equations. We show that in a parallel magnetic field and/or in the presence of supercurrent the transition from superconducting to normal phase occurs as a cascade of discontinuous jumps in the superconducting order parameter for diameters D < 10 divided by 15 nm at T = 0. The critical magnetic field exhibits quantum-size oscillations with pronounced resonant enhancements.