Abstract: At the interface of electrostatic potential kink profiles, one-dimensional chiral states are found in bilayer graphene (BLG). Such structures can be created by applying an asymmetric potential to the upper and the lower layers of BLG. We found the following: (i) due to the strong confinement by the single kink profile, the unidirectional states are only weakly affected by a magnetic field; (ii) increasing the smoothness of the kink potential results in additional bound states, which are topologically different from those chiral states; and (iii) in the presence of a kink-antikink potential, the overlap between the oppositely moving chiral states results in the appearance of crossing and anticrossing points in the energy spectrum. This leads to the opening of tunable minigaps in the spectrum of the unidirectional topological states.

Abstract: The influence of an ellipsoid on the angular order of two-dimensional classical clusters is investigated through Brownian dynamics simulations. We found the following: (1) The presence of an ellipsoid does not influence the start of the angular melting, but reduces the rate at which the inner rings can rotate with respect to each other. (2) Even a small eccentricity of the ellipsoid leads to a stabilization of the angular order of the system. (3) Depending on the position of the ellipsoid in the cluster, a reentrant behavior in the angular order is observed before full radial melting of the cluster sets in. (4) The ellipsoid can lead to a two-step angular melting process: First, the rotation of the inner rings with respect to each other is hindered by the ellipsoid, but on further increasing the kinetic energy of the system, the ellipsoid just starts to behave as a spherical particle with different mobility. The effect of an ellipsoid on the molten system does not depend crucially on the interparticle interaction, but a softer parabolic confinement reduces the angular stabilization.

Abstract: The Dirac equation is solved for triangular and hexagonal graphene quantum dots for different boundary conditions in the presence of a perpendicular magnetic field. We analyze the influence of the dot size and its geometry on their energy spectrum. A comparison between the results obtained for graphene dots with zigzag and armchair edges, as well as for infinite-mass boundary condition, is presented and our results show that the type of graphene dot edge and the choice of the appropriate boundary conditions have a very important influence on the energy spectrum. The single-particle energy levels are calculated as a function of an external perpendicular magnetic field that lifts degeneracies. Comparing the energy spectra obtained from the tight-binding approximation to those obtained from the continuum Dirac equation approach, we verify that the behavior of the energies as a function of the dot size or the applied magnetic field are qualitatively similar, but in some cases quantitative differences can exist.

Abstract: The electronic spectrum of three coupled graphene layers (graphene trilayers) is investigated in the presence of an external magnetic field. We obtain analytical expressions for the Landau level spectrum for both the ABA and ABC type of stacking, which exhibit very different dependence on the magnetic field. We show that layer asymmetry and an external gate voltage can strongly influence the properties of the system.

Abstract: We investigate how the interplay of quantum confinement and particle number-parity fluctuations affects superconducting correlations in ultra-small metallic grains. Using the number-parity projected BCS formalism we calculate the critical temperature and the excitation gap as a function of the grain size for grains with even and odd number of confined carriers. We show that the experimentally observed anomalous increase of the coupling ratio ΔE/kBTc with decreasing superconducting grain size can be attributed to an enhancement of the number-parity fluctuations in ultra-small grains.

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: We propose an effective potential for an excess electron near the helium liquid-vapor interface that takes into account the diffuseness of the liquid-vapor interface and the classical image potential. The splitting of the first two excited states of the excess electron bound to the helium liquid-vapor interface as a function of an external constant electric field applied perpendicular to the interface is in excellent agreement with recent experiments. The effect of a parallel magnetic field on the energy levels are calculated. Single-electron tunneling of the electron out of its surface state is studied as a function of the electric field applied to the system. We found that the tunneling time has a linear dependence on the electric field.

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: We present a model of pressure effects of a two-band superconductor based on a Ginzburg-Landau free energy with two order parameters. The parameters of the theory are pressure as well as temperature dependent. New pressure effects emerge as a result of the competition between the two bands. The theory then is applied to MgB2. We identify two possible scenaria regarding the fate of the two Q subbands under pressure, depending on whether or not both subbands are above the Fermi energy at ambient pressure. The splitting of the two subbands is probably caused by the E-2g, distortion. If only one subband is above the Fermi energy at ambient pressure (scenario I), application of pressure diminishes the splitting and it is possible that the lower subband participates in the superconductivity. The corresponding crossover pressure and Gruneisen parameter are estimated. In the second scenario both bands start above the Fermi energy and they move below it, either by pressure or via the substitution of Mg by Al. In both scenaria, the possibility of electronical topological transition is emphasized. Experimental signatures of both scenaria are presented and existing experiments are discussed in the light of the different physical pictures.