Locally-gated single-layer graphene sheets have unusual discrete energy states inside the potential barrier induced by a finite-width gate. These states are localized outside the Dirac cone of continuum states and are responsible for novel quantum tr
ansport phenomena. Specifically, the longitudinal (along the barrier) conductance exhibits oscillations as a function of barrier height and/or width, which are both controlled by a nearby gate. The origin of these oscillations can be traced back to singularities in the density of localized states. These graphene conductance-oscillations resemble the Shubnikov-de-Haas (SdH) magneto-oscillations; however, here these are driven by an electric field instead of a magnetic field.
We predict surface electromagnetic waves propagating across the layers of intrinsic Josephson junctions. We find the spectrum of the surface waves and study the distribution of the electromagnetic field inside and outside the superconductor. The prof
ile of the amplitude oscillations of the electric field component of such waves is peculiar: initially, it increases toward the center of the superconductor and, after reaching a crossover point, decreases exponentially.
