Conductance Fluctuations, Weak Localization, and Shot Noise for a Ballistic Constriction in a Disordered Wire

This is a study of phase-coherent conduction through a ballistic point contact with disordered leads. The disorder imposes mesoscopic (sample-to-sample) fluctuations and weak-localization corrections on the conductance, and also leads to time-dependent fluctuations (shot noise) of the current. These effects are computed by means of a mapping onto an unconstricted conductor with a renormalized mean free path. The mapping holds both in the metallic and in the localized regime, and permits a solution for arbitrary ratio of mean free path to sample length. In the case of a single-channel quantum point contact, the mapping is onto a one-dimensional disordered chain, for which the complete distribution of the conductance is known. The theory is supported by numerical simulations. ***Submitted to Physical Review B.****Comment: 15 pages, REVTeX-3.0, 9 postscript figures appended as self-extracting archive, INLO-PUB-940309

Tail States below the Thouless Gap in SNS junctions: Classical Fluctuations

We study the tails of the density of states (DOS) in a diffusive superconductor-normal metal-superconductor (SNS) junction below the Thouless gap. We show that long-wave fluctuations of the concentration of impurities in the normal layer lead to the formation of subgap quasiparticle states, and calculate the associated subgap DOS in all effective dimensionalities. We compare the resulting tails with those arising from mesoscopic gap fluctuations, and determine the dimensionless parameters controlling which contribution dominates the subgap DOS. We observe that the two contributions are formally related to each other by a dimensional reduction.Comment: 6 pages, 1 figur

Density of States and Energy Gap in Andreev Billiards

We present numerical results for the local density of states in semiclassical Andreev billiards. We show that the energy gap near the Fermi energy develops in a chaotic billiard. Using the same method no gap is found in similar square and circular billiards.Comment: 9 pages, 6 Postscript figure

Quantum-to-classical crossover for Andreev billiards in a magnetic field

We extend the existing quasiclassical theory for the superconducting proximity effect in a chaotic quantum dot, to include a time-reversal-symmetry breaking magnetic field. Random-matrix theory (RMT) breaks down once the Ehrenfest time $\tau_E$ becomes longer than the mean time $\tau_D$ between Andreev reflections. As a consequence, the critical field at which the excitation gap closes drops below the RMT prediction as $\tau_E/\tau_D$ is increased. Our quasiclassical results are supported by comparison with a fully quantum mechanical simulation of a stroboscopic model (the Andreev kicked rotator).Comment: 11 pages, 10 figure

Commensurability effects in Andreev antidot billiards

An Andreev billiard was realized in an array of niobium filled antidots in a high-mobility InAs/AlGaSb heterostructure. Below the critical temperature T_C of the Nb dots we observe a strong reduction of the resistance around B=0 and a suppression of the commensurability peaks, which are usually found in antidot lattices. Both effects can be explained in a classical Kubo approach by considering the trajectories of charge carriers in the semiconductor, when Andreev reflection at the semiconductor-superconductor interface is included. For perfect Andreev reflection, we expect a complete suppression of the commensurability features, even though motion at finite B is chaotic.Comment: 4 pages, 4 figure

Andreev Conductance of Chaotic and Integrable Quantum Dots

We examine the voltage V and magnetic field B dependent Andreev conductance of a chaotic quantum dot coupled via point contacts to a normal metal and a superconductor. In the case where the contact to the superconductor dominates, we find that the conductance is consistent with the dot itself behaving as a superconductor-- it appears as though Andreev reflections are occurring locally at the interface between the normal lead and the dot. This is contrasted against the behaviour of an integrable dot, where for a similar strong coupling to the superconductor, no such effect is seen. The voltage dependence of the Andreev conductance thus provides an extremely pronounced quantum signature of the nature of the dot's classical dynamics. For the chaotic dot, we also study non-monotonic re-entrance effects which occur in both V and B.Comment: 13 pages, 9 figure

Superconductor-proximity effect in chaotic and integrable billiards

We explore the effects of the proximity to a superconductor on the level density of a billiard for the two extreme cases that the classical motion in the billiard is chaotic or integrable. In zero magnetic field and for a uniform phase in the superconductor, a chaotic billiard has an excitation gap equal to the Thouless energy. In contrast, an integrable (rectangular or circular) billiard has a reduced density of states near the Fermi level, but no gap. We present numerical calculations for both cases in support of our analytical results. For the chaotic case, we calculate how the gap closes as a function of magnetic field or phase difference.Comment: 4 pages, RevTeX, 2 Encapsulated Postscript figures. To be published by Physica Scripta in the proceedings of the "17th Nordic Semiconductor Meeting", held in Trondheim, June 199

Quantum Transparency of Anderson Insulator Junctions: Statistics of Transmission Eigenvalues, Shot Noise, and Proximity Conductance

We investigate quantum transport through strongly disordered barriers, made of a material with exceptionally high resistivity that behaves as an Anderson insulator or a ``bad metal'' in the bulk, by analyzing the distribution of Landauer transmission eigenvalues for a junction where such barrier is attached to two clean metallic leads. We find that scaling of the transmission eigenvalue distribution with the junction thickness (starting from the single interface limit) always predicts a non-zero probability to find high transmission channels even in relatively thick barriers. Using this distribution, we compute the zero frequency shot noise power (as well as its sample-to-sample fluctuations) and demonstrate how it provides a single number characterization of non-trivial transmission properties of different types of disordered barriers. The appearance of open conducting channels, whose transmission eigenvalue is close to one, and corresponding violent mesoscopic fluctuations of transport quantities explain at least some of the peculiar zero-bias anomalies in the Anderson-insulator/superconductor junctions observed in recent experiments [Phys. Rev. B {\bf 61}, 13037 (2000)]. Our findings are also relevant for the understanding of the role of defects that can undermine quality of thin tunnel barriers made of conventional band-insulators.Comment: 9 pages, 8 color EPS figures; one additional figure on mesoscopic fluctuations of Fano facto