Abstract: It is well known that the formation of discrete electron levels strongly influences the pairing in metallic nanograins. Here, we focus on another effect of quantum confinement in superconducting grains that was not studied previously, i.e., spatially nonuniform pairing. This effect is very significant when single-electron levels form bunches and/or a kind of shell structure. We find that, in highly symmetric grains, the order parameter can exhibit variations with position by an order of magnitude. Nonuniform pairing is closely related to a quantum-confinement-induced modification of the pairing-interaction matrix elements and size-dependent pinning of the chemical potential to groups of degenerate or nearly degenerate levels. For illustrative purposes, we consider spherical metallic nanograins and also rectangular shapes. We show that the relevant matrix elements are, as a rule, enhanced in the presence of quantum confinement, which favors spatial variations of the order parameter, compensating the corresponding energy cost. The size-dependent pinning of the chemical potential further increases the spatial variation of the pair condensate. The role of nonuniform pairing is smaller in less symmetric confining geometries and/or in the presence of disorder. However, it always remains of importance when the energy spacing between discrete electron levels δ is approaching the scale of the bulk gap ΔB, i.e., δ>0.10.2 ΔB.

Abstract: The crystallographic structure and the distribution of orientations of molecular ions are studied near the surface in an orientationally disordered crystal with the use of a Green-function formalism. The orientational degrees of freedom are treated by means of symmetry-adapted functions of angular coordinates. The structure of the (001) surface of KCN in its cubic fcc phase is then predicted using the existing data on the interaction of the ions K+ and CN-. A local antiferroelectric and antiferroelastic order i shown to exist in the surface region. The magnitude of the order and the spatial extent of the ordered re ion increase as the temperature approaches the point of the phase transition to the ordered phase. The,influence of the external electric field on the structure of the surface is predicted.

Abstract: We have developed a microscopic theory which describes the orientational dynamics of C60 molecules in the face-centered-cubic phase of C60 fullerite. The molecular interaction potential and the crystal-field potential are formulated in terms of symmetry-adapted rotator functions. The phase transition to the Pa3BAR structure is driven by an active multipolar mode of T2g symmetry belonging to the l = 10 manifold. The Birman criterion is satisfied. The transition is found to be of first order.

Abstract: Starting from a model of microscopic interactions between C-70 molecules, we have developed a theory which describes the orientational dynamics and its coupling to lattice displacements in the rhombohedral phase of C-70 fullerite. The Landau free energy is calculated. We obtain a first-order phase transition to a monoclinic structure with the space group P2(1)/m. The transition is driven by the condensation of orientational quadrupoles at the F point of the Brillouin zone of the rhombohedral lattice. We find no evidence that the monoclinic structure is connected with the freezing in of orientations around the fivefold molecular axis. We calculate the lattice strains that are associated with the transition to the monoclinic structure. The theory is compared with a range of experimental data on the phase transition.

Abstract: We numerically investigate the mixed pairing symmetries inmesoscopic superconducting loops in the presence of spin correlations by solving the Bogoliubov-de Gennes equations self-consistently. The spatial variations of the superconducting order parameters and the spontaneous magnetization are determined by the band structure. When the threaded magnetic flux turns on, the charge and spin currents both emerge and depict periodic evolution. In the case of a mesoscopic loop with dominant triplet p(x) +/- ip(y)-wave symmetry, a slight change of the chemical potential may lead to novel flux-dependent evolution patterns of the ground-state energy and the magnetization. The spin-polarized currents show pronounced quantum oscillations with fractional periods due to the appearance of energy jumps in flux, accompanied with a steplike feature of the enhanced spin current. Particularly, at some appropriate flux, the peaks of the zero-energy local density of states clearly indicate the occurrence of the odd-frequency pairing. In the case of a superconducting loop with dominant singlet d(x2-y2)-wave symmetry, the spatial profiles of the zero-energy local density of states and the magnetization show spin-dependent features on different sample diagonals. Moreover, the evolution of the flux-induced spin current always exhibits an hc/e periodicity.

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 present model calculations based on a coherent tunneling picture, which reproduce well both the single-particle energy level position and the resonant current strength at two typical anticrossings, one involving two levels and the other three levels in a coherent mixer composed of two weakly coupled vertical quantum dots. An essential ingredient is the inclusion of higher degree terms to account for deviations from an ideal elliptical parabolic confining potential in realistic dots. We also calculate density plots of the mixed states for the modified potential.