Advanced simulation of conductance histograms validated through channel-sensitive experiments on indium nanojunctions.

We demonstrate a self-contained methodology for predicting conductance histograms of atomic and molecular junctions. Fast classical molecular-dynamics simulations are combined with accurate density functional theory calculations predicting both quantum transport properties and molecular-dynamics force field parameters. The methodology is confronted with experiments on atomic-sized indium nanojunctions. Beside conductance histograms the distribution of individual channel transmission eigenvalues is also determined by fitting the superconducting subgap features in the I-V curves. The remarkable agreement in the evolution of the channel transmissions demonstrates that the simulated ruptures are able to reproduce a realistic statistical ensemble of contact configurations, whereas simulations on selected ideal geometries show strong deviations from the experimental observations.

Quantum-classical correspondence in the wave functions of andreev billiards.

We present a classical and quantum mechanical study of an Andreev billiard with a chaotic normal dot. We demonstrate that the nonexact velocity reversal and the diffraction at the edges of the normal-superconductor contact render the classical dynamics of these systems mixed indicating the limitations of a widely used retracing approximation. We point out the close relation between the mixed classical phase space and the properties of the quantum states of Andreev billiards, including periodic orbit scarring and localization of the wave function onto other classical phase space objects such as intermittent regions and quantized tori.

Proximity-induced subgaps in andreev billiards.

We examine the density of states of an Andreev billiard and show that any billiard with a finite upper cutoff in the path length distribution P(s) will possess an energy gap on the scale of the Thouless energy. An exact quantum mechanical calculation for different Andreev billiards gives good agreement with the semiclassical predictions when the energy dependent phase shift for Andreev reflections is properly taken into account. Based on this new semiclassical Bohr-Sommerfeld approximation of the density of states, we derive a simple formula for the energy gap. We show that the energy gap, in units of Thouless energy, may exceed the value predicted earlier from random matrix theory for chaotic billiards.

Negative length orbits in normal-superconductor billiard systems

The path-length spectra of mesoscopic systems including diffractive scatterers and connected to a superconductor are studied theoretically. We show that the spectra differ fundamentally from that of normal systems due to the presence of Andreev reflection. It is shown that negative path lengths should arise in the spectra as opposed to the normal system. To highlight this effect we carried out both quantum mechanical and semiclassical calculations for the simplest possible diffractive scatterer. The most pronounced peaks in the path-length spectra of the reflection amplitude are identified by the routes that the electron and/or hole travels.