Abstract: We investigate the superconducting states that arise as a consequence of mesoscopic confinement and a multicomponent order parameter in the Ginzburg-Landau model for p-wave superconductivity. Conventional vortices, but also half-quantum vortices and skyrmions, are found as the applied magnetic field and the anisotropy parameters of the Fermi surface are varied. The solutions are well differentiated by a topological charge that for skyrmions is given by the Hopf invariant and for vortices by the circulation of the superconducting velocity. We revealed several unique states combining vortices and skyrmions, their possible reconfiguration with varied magnetic field, as well as temporal and field-induced transitions between vortical and skyrmionic states.

Abstract: Dynamics of electron wave-packets is studied using the continuum Dirac model in a graphene geometric diode where the propagation of the wave packet is favored in certain direction due to the presence of geometric constraints. Clear rectification is obtained in the THz frequency range with the maximum rectification level of 3.25, which is in good agreement with recent experiments on graphene ballistic diodes. The rectification levels are considerably higher for systems with narrower channels. In this case, the wave packet transmission probabilities and rectification rate also strongly depend on the energy of the incident wave packet, as a result of the quantum nature of energy levels along such channels. These findings can be useful for fundamental understanding of the charge carrier dynamics in graphene geometry diodes.

Abstract: The moire pattern observed in stacked noncommensurate crystal lattices, such as heterobilayers of transition metal dichalcogenides, produces a periodic modulation of their band gap. Excitons subjected to this potential landscape exhibit a band structure that gives rise to a quasiparticle dubbed the moire exciton. In the case of MoS2/WSe2 heterobilayers, the moire trapping potential has honeycomb symmetry and, consequently, the moire exciton band structure is the same as that of a Dirac-Weyl fermion, whose mass can be further tuned down to zero with a perpendicularly applied field. Here we show that, analogously to other Dirac-like particles, the moire exciton exhibits a trembling motion, also known as Zitterbewegung, whose long timescales are compatible with current experimental techniques for exciton dynamics. This promotes the study of the dynamics of moire excitons in van der Waals heterostructures as an advantageous solid-state platform to probe Zitterbewegung, broadly tunable by gating and interlayer twist angle.