Non-adiabatic Josephson Dynamics in Junctions with in-Gap Quasiparticles

Conventional models of Josephson junction dynamics rely on the absence of low energy quasiparticle states due to a large superconducting gap. With this assumption the quasiparticle degrees of freedom become "frozen out" and the phase difference becomes the only free variable, acting as a fictitious particle in a local in time Josephson potential related to the adiabatic and non-dissipative supercurrent across the junction. In this article we develop a general framework to incorporate the effects of low energy quasiparticles interacting non-adiabatically with the phase degree of freedom. Such quasiparticle states exist generically in constriction type junctions with high transparency channels or resonant states, as well as in junctions of unconventional superconductors. Furthermore, recent experiments have revealed the existence of spurious low energy in-gap states in tunnel junctions of conventional superconductors - a system for which the adiabatic assumption typically is assumed to hold. We show that the resonant interaction with such low energy states rather than the Josephson potential defines nonlinear Josephson dynamics at small amplitudes.Comment: 9 pages, 1 figur

Multiple Andreev Reflections in Weak Links of Superfluid 3He-B

We calculate the current-pressure characteristics of a ballistic pinhole aperture between two volumes of B-phase superfluid 3He. The most important mechanism contributing to dissipative currents in weak links of this type is the process of multiple Andreev reflections. At low biases this process is significantly affected by relaxation due to inelastic quasiparticle-quasiparticle collisions. In the numerical calculations, suppression of the superfluid order parameter at surfaces is taken into account self-consistently. When this effect is neglected, the theory may be developed analytically like in the case of s-wave superconductors. A comparison with experimental results is presented.Comment: 12 pages, 9 figures, RevTeX

Transport Processes in Metal-Insulator Granular Layers

Tunnel transport processes are considered in a square lattice of metallic nanogranules embedded into insulating host to model tunnel conduction in real metal/insulator granular layers. Based on a simple model with three possible charging states ($\pm$, or 0) of a granule and three kinetic processes (creation or recombination of a $\pm$ pair, and charge transfer) between neighbor granules, the mean-field kinetic theory is developed. It describes the interplay between charging energy and temperature and between the applied electric field and the Coulomb fields by the non-compensated charge density. The resulting charge and current distributions are found to be essentially different in the free area (FA), between the metallic contacts, or in the contact areas (CA), beneath those contacts. Thus, the steady state dc transport is only compatible with zero charge density and ohmic resistivity in FA, but charge accumulation and non-ohmic behavior are \emph{necessary} for conduction over CA. The approximate analytic solutions are obtained for characteristic regimes (low or high charge density) of such conduction. The comparison is done with the measurement data on tunnel transport in related experimental systems.Comment: 10 pages, 11 figures, 1 reference corrected, acknowlegments adde

Josephson effect in graphene SBS junctions

We study Josephson effect in graphene superconductor- barrier- superconductor junctions with short and wide barriers of thickness $d$ and width $L$, which can be created by applying a gate voltage $V_0$ across the barrier region. We show that Josephson current in such graphene junctions, in complete contrast to their conventional counterparts, is an oscillatory function of both the barrier width $d$ and the applied gate voltage $V_0$. We also demonstrate that in the thin barrier limit, where $V_0 \to \infty$ and $d \to 0$ keeping $V_0 d$ finite, such an oscillatory behavior can be understood in terms of transmission resonance of Dirac-Bogoliubov-de Gennes quasiparticles in superconducting graphene. We discuss experimental relevance of our work.Comment: 7 Pg., 6 Figs, extended version submitted to PR

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

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

Spectrum of Andreev Bound States in a Molecule Embedded Inside a Microwave-Excited Superconducting Junction

Non-dissipative Josephson current through nanoscale superconducting constrictions is carried by spectroscopically sharp energy states, so-called Andreev bound states. Although theoretically predicted almost 40 years ago, no direct spectroscopic evidence of these Andreev bound states exists to date. We propose a novel type of spectroscopy based on embedding a superconducting constriction, formed by a single-level molecule junction, in a microwave QED cavity environment. In the electron-dressed cavity spectrum we find a polariton excitation at twice the Andreev bound state energy, and a superconducting-phase dependent ac Stark shift of the cavity frequency. Dispersive measurement of this frequency shift can be used for Andreev bound state spectroscopy.Comment: Published version; 4+ pages, 3 figure

Excitation gap of a graphene channel with superconducting boundaries

We calculate the density of states of electron-hole excitations in a superconductor/normal-metal/superconductor (SNS) junction in graphene, in the long-junction regime that the superconducting gap is much larger than the Thouless energy. If the normal region is undoped, the excitation spectrum consists of neutral modes that propagate along the boundaries - transporting energy but no charge. These ``Andreev modes'' are a coherent superposition of electron states from the conduction band and hole states from the valence band, coupled by specular Andreev reflection at the superconductor. The lowest Andreev mode has an excitation gap, which depends on the superconducting phase difference across the SNS graphene channel. At high doping the excitation gap vanishes and the usual gapless density of states of Andreev levels is recovered. We use our results to calculate the superconducting phase dependence of the thermal conductance of the graphene channel.Comment: 8 pages, 10 figure

Conductance of a STM contact on the surface of a thin film

The conductance of a contact, having a radius smaller than the Fermi wave length, on the surface of a thin metal film is investigated theoretically. It is shown that quantization of the electron energy spectrum in the film leads to a step-like dependence of differential conductance G(V) as a function of applied bias eV. The distance between neighboring steps in eV equals the energy level spacing due to size quantization. We demonstrate that a study of G(V) for both signs of the voltage maps the spectrum of energy levels above and below Fermi surface in scanning tunneling experiments.Comment: 15 pages, 5 figure

Meta-analytic Findings on Grouping Programs

Meta-analytic reviews have focused on five distinct instructional programs that separate students by ability: multilevel dasses, cross-grade programs, within-class grouping, enriched classes for the gifted and talented, and accelerated classes. The reviews show that effects are a function of program type. Multilevel classes, which entail only minor adjustment of course content for ability groups, usually have little or no effect on student achievement. Programs that entail more substantial adjustment of curriculum to ability, such as cross-grade and within-class programs, produce clear positive effects. Programs of enrichment and acceleration, which usually involve the greatest amount of curricular adjustment, have the largest effects on student learning. These results doe not support recent claims that no one benefits from grouping or that students in the lower groups are harmed academically and emotionally by grouping.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67315/2/10.1177_001698629203600204.pd