Abstract: We investigate mesoscopic Josephson-junction arrays created by patterning superconducting disks on monolayer graphene, concentrating on the high-T/T-c regime of these devices and the phenomena which contribute to the superconducting glass state in diffusive arrays. We observe features in the magnetoconductance at rational fractions of flux quanta per array unit cell, which we attribute to the formation of flux-quantized vortices. The applied fields at which the features occur are well described by Ginzburg-Landau simulations that take into account the number of unit cells in the array. We find that the mean conductance and universal conductance fluctuations are both enhanced below the critical temperature and field of the superconductor, with greater enhancement away from the graphene Dirac point.

Abstract: Bogoliubov-de Gennes theory is used to investigate the effect of the size of a superconducting square on the vortex states in the quantum confinement regime. When the superconducting coherence length is comparable to the Fermi wavelength, the shape resonances of the superconducting order parameter have strong influence on the vortex configuration. Several unconventional vortex states, including asymmetric ones, giant-multivortex combinations, and states comprising giant antivortices, were found as ground states and their stability was found to be very sensitive on the value of k(F)xi(0), the size of the sample W, and the magnetic flux Phi. By increasing the temperature and/or enlarging the size of the sample, quantum confinement is suppressed and the conventional mesoscopic vortex states as predicted by the Ginzburg-Laudau (GL) theory are recovered. However, contrary to the GL results we found that the states containing symmetry-induced vortex-antivortex pairs are stable over the whole temperature range. It turns out that the inhomogeneous order parameter induced by quantum confinement favors vortex-antivortex molecules, as well as giant vortices with a rich structure in the vortex core-unattainable in the GL domain.

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.