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: 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: The vortex-vortex interaction potential in bulk superconductors is calculated within the Ginzburg-Landau (GL) theory and is obtained from a numerical solution of a set of two coupled nonlinear GL differential equations for the vector potential and the superconducting order parameter, where the merger of vortices into a giant vortex is allowed. Further, the interaction potentials between a vortex and a giant vortex and between a vortex and an antivortex are obtained for both type-I and type-II superconductors. Our numerical results agree asymptotically with the analytical expressions for large intervortex separations that are available in the literature. We propose empirical expressions valid over the full interaction range, which are fitted to our numerical data for different values of the GL parameter.

Abstract: The time evolution of a wave packet in strained graphene is studied within the tight-binding model and continuum model. The effect of an external magnetic field, as well as a strain-induced pseudomagnetic field, on the wave-packet trajectories and zitterbewegung are analyzed. Combining the effects of strain with those of an external magnetic field produces an effective magnetic field which is large in one of the Dirac cones, but can be practically zero in the other. We construct an efficient valley filter, where for a propagating incoming wave packet consisting of momenta around the K and K' Dirac points, the outgoing wave packet exhibits momenta in only one of these Dirac points while the components of the packet that belong to the other Dirac point are reflected due to the Lorentz force. We also found that the zitterbewegung is permanent in time in the presence of either external or strain-induced magnetic fields, but when both the external and strain-induced magnetic fields are present, the zitterbewegung is transient in one of the Dirac cones, whereas in the other cone the wave packet exhibits permanent spatial oscillations.

Abstract: The time evolution of a wave packet injected into a semiconductor quantum ring is investigated in order to obtain the transmission and reflection probabilities. Within the effective-mass approximation, the time-dependent Schrödinger equation is solved for a system with nonzero width of the ring and leads and finite potential-barrier heights, where we include smooth lead-ring connections. In the absence of a magnetic field, an analysis of the projection of the wave function over the different subband states shows that when the injected wave packet is within a single subband, the junction can scatter this wave packet into different subbands but remarkably at the second junction the wave packet is scattered back into the subband state of the incoming wave packet. If a magnetic field is applied perpendicularly to the ring plane, transmission and reflection probabilities exhibit Aharonov-Bohm (AB) oscillations and the outgoing electrons may end up in different subband states from those of the incoming electrons. Localized impurities, placed in the ring arms, influence the AB oscillation period and amplitude. For a single impurity or potential barrier of sufficiently strong strength, the period of the AB oscillations is halved while for two impurities localized in diametrically opposite points of the ring, the original AB period is recovered. A theoretical investigation of the confined states and time evolution of wave packets in T wires is also made, where a comparison between this system and the lead-ring junction is drawn.

Abstract: Using the four-band continuum model we derive a general expression for the infinite-mass boundary condition in bilayer graphene. Applying this new boundary condition we analytically calculate the confined states and the corresponding wave functions in a bilayer graphene quantum dot in the absence and presence of a perpendicular magnetic field. Our results for the energy spectrum show an energy gap between the electron and hole states at small magnetic fields. Furthermore the electron (e) and hole (h) energy levels corresponding to the K and K' valleys exhibit the E-K(e(h)) (m) = E-K'(e(h)) (m) symmetry, where m is the angular momentum quantum number. (C) 2014 Elsevier Ltd. All rights reserved.

Abstract: The thermal properties of a two-dimensional classical cluster of negatively charged particles bound by a punctual positive charge are presented. The melting phenomenon is analyzed and the features which characterize such a solid-liquid transition are highlighted. We found that the presence of metastable states strongly modifies the melting scenario, and that the melting temperature of the system is determined by the height of the saddle point energy separating the ground state and the metastable state. Due to the particular type of confinement potential considered in this paper, we also found that, at sufficiently large temperature, the cluster can become thermally ionized.