Abstract: The effect of a parallel magnetic field on the orbital motion of electrons in high-quality superconducting nanowires resulting in a superconductor-to-normal transition which occurs through a cascade of jumps in the order parameter as a function of the magnetic field. Such cascades originate from the transverse size quantization that splits the conduction band into a series of subbands. Here, based on a numerical solution of the Bogoliubov-de Gennes equations for a hollow nanocylinder, we investigate how the quantum-size cascades depend on the confining geometry, i.e., by changing the cylinder radius R and its thickness d we cover the range from the nanowire-like to the nanofilm-like regime. The cascades are shown to become much less pronounced when increasing R/d, i.e., when the nanofilm-like regime is approached. When the temperature is non-zero they are thermally smoothed. This includes the spin-magnetic-field interaction which reduces the critical (depairing) parallel magnetic field H-c,H-parallel to but does not have any qualitative effect on the quantum cascades. From our calculations it is seen that the paramagnetic limiting field H-par significantly exceeds H-c,H-parallel to even in extremely narrow nanocylinders, i.e., when R, d are down to a few nanometers, and H-c,H-parallel to is only about 10% larger when switching-off the spin-magnetic-field interaction in this case. Both characteristic fields, H-c,H-parallel to and H-par, exhibit pronounced quantum-size oscillations. We demonstrate that the quantum cascades and the quantum-size oscillations survive in the presence of surface roughness.

Abstract: Since the 1960's it has been well known that the basic superconductive quantities can exhibit oscillations as functions of the thickness (diameter) in superconducting nanofilms (nanowires) due to the size quantization of the electronic spectrum. However, very little is known about the effects of quantum confinement on the microscopic properties of vortices. Based on a numerical solution to the Bogoliubov-de Gennes equations, we study the quantum-size oscillations of the vortex core resulting from the sequential interchange of the Kramer-Pesch and anti-Kramer-Pesch regimes with changing nanocylinder radius. The physics behind the anti-Kramer-Pesch anomaly is displayed by utilizing a semi-analytical Anderson approximate solution. We also demonstrate that the anti-Kramer-Pesch vortex core is robust against thermal smearing and results in a distinctive two-maxima structure in the local density of states, which can be used to identify the existence of the anti-Kramer-Pesch vortex.

Abstract: Electrical transport properties of a two-dimensional electron gas axe studied in the presence of a perpendicular magnetic field B modulated weakly and periodically along one direction, B = (B + B0 cos Kx)z, with B0 much less than B, K = 2pi/a, and a being the period of the modulation. B0 is taken constant or proportional to B. The Landau levels broaden into bands and their width, proportional to the modulation strength B0, oscillates with B and gives rise to oscillations in the magnetoresistance at low B. These oscillations reflect the commensurability between the cyclotron diameter at the Fermi level and the period a and consequently hey are distinctly different from the Shubnikov-de Ha.as ones, at higher B, in period and temperature dependence. The bandwidth at the Fermi energy can be one order of magnitude larger, at low B, than that of the electric case for equal modulation strengths. The resulting magnetoresistance oscillations have a much higher amplitude than those of the electric case with which they are out of phase. Explicit asymptotic expressions are derived for the temperature dependence of the transport coefficients. The case when both electric and magnetic modulations are present is also considered. 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: Pinning of magnetic-field-induced Wigner molecules (WMs) confined in parabolic two-dimensional quantum dots by a charged defect is studied by an exact diagonalization approach. We found a re-entrant pinning of the WMs as a function of the magnetic field, a magnetic-field-induced re-orientation of the WMs and a qualitatively different pinning behaviour in the presence of a positive and negative Coulomb impurity.

Abstract: We report an anomalous matching effect in MoGe thin films containing pairs of circular holes arranged in such a way that four of those pairs meet at each vertex point of a square lattice. A remarkably pronounced fractional matching was observed in the magnetic field dependences of both the resistance and the critical current. At the half matching field the critical current can be even higher than that at zero field. This has never been observed before for vortices in superconductors with pinning arrays. Numerical simulations within the nonlinear Ginzburg-Landau theory reveal a square vortex ice configuration in the ground state at the half matching field and demonstrate similar characteristic features in the field dependence of the critical current, confirming the experimental realization of an artificial ice system for vortices for the first time.

Abstract: A Josephson phase shift can be induced in a Josephson junction by a strategically nearby pinned Abrikosov vortex (AV). For an asymmetric distribution of an imprinted phase along the junction (controlled by the position of the AV) such a simple system is capable of rectification of ac current in a broad and tunable frequency range. The resulting rectified voltage is a consequence of the directed motion of a Josephson antivortex which forms a pair with the AV when at local equilibrium. The proposed realization of the ratchet potential by an imprinted phase is more efficient than the asymmetric geometry of the junction itself, is easily realizable experimentally, and provides rectification even in the absence of an applied magnetic field.

Abstract: The Coulomb interaction and the correlation of a remote electron with a single layer of graphene is investigated in the presence of a magnetic field applied perpendicular to the graphene layer. The remote electron polarizes the electron gas in the graphene layer, which we describe in terms of excitations of virtual plasmons in graphene. The composite quasiparticle formed by electron plus polarization is called a plasmon polaron. The ground-state energy of this quasiparticle is calculated within perturbation theory for remote electrons in different environments.