Abstract: Superconductivity is a macroscopic coherent state exhibiting various quantum phenomena such as magnetic flux quantization. When a superconducting ring is placed in a magnetic field, a current flows to expel the field from the ring and to ensure that the enclosed flux is an integer multiple of h/(2|e|). Although the quantization of magnetic flux in ring structures is extensively studied in literature, the applied magnetic field is typically assumed to be homogeneous, implicitly implying an interplay between field expulsion and flux quantization. Here, we propose to decouple these two effects by employing an Aharonov-Bohm-like structure where the superconducting ring is threaded by a magnetic core (to which the applied field is confined). Although the magnetic field vanishes inside the ring, the formation of vortices takes place, corresponding to a change in the flux state of the ring. The time evolution of the density of superconducting electrons is studied using the time-dependent Ginzburg-Landau equations.

Abstract: Ultranarrow superconductors are in the strong quantum confinement regime with formation of multiple coherent condensates associated with the many subbands of the electronic structure. Here, we analyze the multiband BCS-BEC crossover induced by the chemical potential tuned close to a subband bottom, in correspondence of a superconducting shape resonance. The evolution of the condensate fraction and of the pair correlation length in the ground state as functions of the chemical potential demonstrates the tunability of the BCS-BEC crossover for the condensate component of the selected subband. The extension of the crossover regime increases when the pairing strength and/or the characteristic energy of the interaction get larger. Our results indicate the coexistence of large and small Cooper pairs in the crossover regime, leading to the optimal parameter configuration for high transition temperature superconductivity.

Abstract: Magnetically coupled superconductorferromagnet hybrids offer advanced routes for nanoscale control of superconductivity. Magnetotransport characteristics and scanning tunneling microscopy images of vortex structures in superconductorferromagnet hybrids reveal rich superconducting phase diagrams. Focusing on a particular combination of a ferromagnet with a well-ordered periodic magnetic domain structure with alternating out-of-plane component of magnetization, and a small coherence length superconductor, we find directed nucleation of superconductivity above the domain wall boundaries. We show that near the superconductor-normal state phase boundary the superconductivity is localized in narrow mesoscopic channels. In order to explore the Abrikosov flux line ordering in F/S hybrids, we use a combination of scanning tunneling microscopy and GinzburgLandau simulations. The magnetic stripe domain structure induces periodic local magnetic induction in the superconductor, creating a series of pinninganti-pinning channels for externally added magnetic flux quanta. Such laterally confined Abrikosov vortices form quasi-1D arrays (chains). The transitions between multichain states occur through propagation of kinks at the intermediate fields. At high fields we show that the system becomes nonlinear due to a change in both the number of vortices and the confining potential. In F/S/F hybrids we demonstrate the evolution of the anisotropic conductivity in the superconductor that is magnetically coupled with two adjacent ferromagnetic layers. Stripe magnetic domain structures in both F-layers are aligned under each other, resulting in a directional superconducting order parameter in the superconducting layer. The conductance anisotropy strongly depends on the period of the magnetic domains and the strength of the local magnetization. The anisotropic conductivity of up to three orders of magnitude can be achieved with a spatial critical temperature modulation of 5% of T c. Induced anisotropic properties in the F/S and F/S/F hybrids have a potential for future application in switching and nonvolatile memory elements operating at low temperatures.

Abstract: The scattering of two-dimensional (2D) massless electrons as presented in graphene in the presence of a random array of circular magnetic flux tubes is investigated. The momentum relaxation time and the Hall factor are obtained using optical theorem techniques for scattering. Electrons with energy close to those of the Landau levels of the flux tubes exhibit resonant scattering and have a long life-time to reside inside the magnetic flux tube. These resonances appear as sharp structures in the Hall factor and the magneto-resistance.

Abstract: The dynamics of electrons and holes propagating through the nano-scaled channels of modern semiconductor devices can be seen as a widespread manifestation of non-equilibrium statistical physics and its ruling principles. In this respect both the devices that are pushing conventional CMOS technology towards the final frontiers of Moores law and the upcoming set of alternative, novel nanostructures grounded on entirely new concepts and working principles, provide an almost unlimited playground for assessing physical models and numerical techniques emerging from classical and quantum mechanical non-equilibrium theory. In this paper we revisit the Boltzmann as well as the WignerBoltzmann equation which offers a valuable platform to study transport of charge carriers taking part in drive currents. We focus on a numerical procedure that regained attention recently as an alternative tool to solve the time-dependent Boltzmann equation for inhomogeneous systems, such as the channel regions of field-effect transistors, and we discuss its extension to the WignerBoltzmann equation. Furthermore, we pay attention to the calculation of tunneling leakage currents. The latter typically occurs in nano-scaled transistors when part of the carrier distribution sustaining the drive current is found to tunnel into the gate due the presence of an ultra-thin insulating barrier separating the gate from the channel region. In particular, we discuss the paradox related to the very existence of leakage currents established by electrons occupying quasi-bound states, while the (real) wave functions of the latter cannot carry net currents. Finally, we describe a simple model to resolve the paradox as well as to estimate gate currents provided the local carrier generation rates largely exceed the tunneling rates.

Abstract: We derive an analytical model for the electrostatics and the drive current in a silicon nanowire operating in JFET mode. We show that there exists a range of nanowire radii and doping densities for which the nanowire JFET satisfies reasonable device characteristics. For thin nanowires we have developed a self-consistent quantum mechanical model to obtain the electronic structure.

Abstract: We introduce a generalized non-equilibrium statistical operator (NSO) to study a current-carrying system. The NSO is used to derive a set of quantum kinetic equations based on quantum mechanical balance equations. The quantum kinetic equations are solved self-consistently together with Poissons equation to solve a general transport problem. We show that these kinetic equations can be used to rederive the Landauer formula for the conductance of a quantum point contact, without any reference to reservoirs at different chemical potentials. Instead, energy dissipation is taken into account explicitly through the electron-phonon interaction. We find that both elastic and inelastic scattering are necessary to obtain the Landauer conductance.