Stability of dynamic coherent states in intrinsic Josephson-junction stacks near internal cavity resonance

Stacks of intrinsic Josephson junctions in the resistive state can by efficiently synchronized by the internal cavity mode resonantly excited by the Josephson oscillations. We study the stability of dynamic coherent states near the resonance with respect to small perturbations. Three states are considered: the homogeneous and alternating-kink states in zero magnetic field and the homogeneous state in the magnetic field near the value corresponding to half flux quantum per junction. We found two possible instabilities related to the short-scale and long-scale perturbations. The homogeneous state in modulated junction is typically unstable with respect to the short-scale alternating phase deformations unless the Josephson current is completely suppressed in one half of the stack. The kink state is stable with respect to such deformations and homogeneous state in the magnetic field is only stable within a certain range of frequencies and fields. Stability with respect to the long-range deformations is controlled by resonance excitations of fast modes at finite wave vectors and typically leads to unstable range of the wave-vectors. This range shrinks with approaching the resonance and increasing the in-plane dissipation. As a consequence, in finite-height stacks the stability frequency range near the resonance increases with decreasing the height.Comment: 15 pages, 8 figures, to appear in Phys. Rev.

Coherent current states in mesoscopic four-terminal Josephson junction

A theory is offered for the ballistic 4-terminal Josephson junction. The studied system consists of a mesoscopic two-dimensional normal rectangular layer which is attached in each side to the bulk superconducting banks (terminals). The relation between the currents through the different terminals, which is valid for arbitrary temperatures and junction sizes, is obtained. The nonlocal coupling of the supercurrents leads to a new effect, specific for the mesoscopic weak link between two superconducting rings; an applied magnetic flux through one of the rings produces a magnetic flux in the other ring even in the absence of an external flux through the other one. The phase dependent distributions of the local density of Andreev states, of the supercurrents and of the induced order parameter are obtained. The "interference pattern" for the anomalous average inside the two dimensional region can be regulated by the applied magnetic fluxes or the transport currents. For some values of the phase differences between the terminals, the current vortex state and the two dimensional phase slip center are appeared.Comment: 17 pages in Latex and 6 ps Figures. Will be published in Low Temp.Phy

Topological confinement in bilayer graphene

We study a new type of one-dimensional chiral states that can be created in bilayer graphene (BLG) by electrostatic lateral confinement. These states appear on the domain walls separating insulating regions experiencing the opposite gating polarity. While the states are similar to conventional solitonic zero-modes, their properties are defined by the unusual chiral BLG quasiparticles, from which they derive. The number of zero-mode branches is fixed by the topological vacuum charge of the insulating BLG state. We discuss how these chiral states can manifest experimentally, and emphasize their relevance for valleytronics.Comment: 4 pages, 3 figure

Voltage dependent conductance and shot noise in quantum microconstriction with single defects

The influence of the interference of electron waves, which are scattered by single impurities and by a barrier on nonlinear conductance and shot noise of metallic microconstriction is studied theoretically. It is shown that the these characteristics are nonmonotonic functions on the applied bias.Comment: 18 pages,5 figure

Phase Modulated Thermal Conductance of Josephson Weak Links

We present a theory for quasiparticle heat transport through superconducting weak links. The thermal conductance depends on the phase difference ($\phi$) of the superconducting leads. Branch conversion processes, low-energy Andreev bound states near the contact and the suppression of the local density of states near the gap edge are related to phase-sensitive transport processes. Theoretical results for the influence of junction transparency, temperature and disorder, on the phase modulation of the conductance are reported. For high-transmission weak links, $D\to 1$, the formation of an Andreev bound state at $\epsilon_{\text{\tiny b}}=\Delta\cos(\phi/2)$ leads to suppression of the density of states for the continuum excitations that transport heat, and thus, to a reduction in the conductance for $\phi\simeq\pi$. For low-transmission ($D\ll 1$) barriers resonant scattering at energies $\epsilon\simeq(1+D/2)\Delta$ leads to an increase in the thermal conductance as $T$ drops below $T_c$ (for phase differences near $\phi=\pi$).Comment: 4 pages, 3 figures Expanded discussion of boundary conditions for Ricatti amplitude

The theory of the reentrant effect in susceptibility of cylindrical mesoscopic samples

A theory has been developed to explain the anomalous behavior of the magnetic susceptibility of a normal metal-superconductor ($NS$) structure in weak magnetic fields at millikelvin temperatures. The effect was discovered experimentally by A.C. Mota et al \cite{10}. In cylindrical superconducting samples covered with a thin normal pure metal layer, the susceptibility exhibited a reentrant effect: it started to increase unexpectedly when the temperature lowered below 100 mK. The effect was observed in mesoscopic $NS$ structures when the $N$ and $S$ metals were in good electric contact. The theory proposed is essentially based on the properties of the Andreev levels in the normal metal. When the magnetic field (or temperature) changes, each of the Andreev levels coincides from time to time with the chemical potential of the metal. As a result, the state of the $NS$ structure experiences strong degeneracy, and the quasiparticle density of states exhibits resonance spikes. This generates a large paramagnetic contribution to the susceptibility, which adds up to the diamagnetic contribution thus leading to the reentrant effect. The explanation proposed was obtained within the model of free electrons. The theory provides a good description for experimental results [10]

Effect of quantum interference in the nonlinear conductance of microconstrictions

The influence of the interference of electron waves, which were scattered by single impurities, on nonlinear quantum conductance of metallic microconstrictions (as was recently investigated experimentally) is studied theoretically. The dependence of the interference pattern in the conductance $G(V)$ on the contact diameter and the spatial distribution of impurities is analyzed. It is shown that the amplitude of conductance oscillation is strongly depended on the position of impurities inside the constriction.Comment: 6 pages, 4 figures, To appear in PR