Subtleties on energy calculations in the image method

In this pedagogical work we point out a subtle mistake that can be done by undergraduate or graduate students in the computation of the electrostatic energy of a system containing charges and perfect conductors if they naively use the image method. Specifically, we show that the naive expressions for the electrostatic energy for these systems obtained directly from the image method are wrong by a factor 1/2. We start our discussion with well known examples, namely, point charge-perfectly conducting wall and point charge-perfectly conducting sphere and then proceed to the demonstration of general results, valid for conductors of arbitrary shapes.Comment: 9 pages, 2 figures; Major change in this version: subsection added to Sect.4 (theorem generalization). Minor changes: title replaced; corrections to the English; some explanatory comments adde

Mesoscopic supercurrent transistor controlled by nonequilibrium cooling

The distinctive quasiparticle distribution existing under nonequilibrium in a superconductor-insulator-normal metal-insulator-superconductor (SINIS) mesoscopic line is proposed as a novel tool to control the supercurrent intensity in a long Josephson weak link. We present a description of this system in the framework of the diffusive-limit quasiclassical Green-function theory and take into account the effects of inelastic scattering with arbitrary strength. Supercurrent enhancement and suppression, including a marked transition to a $\pi$-junction are striking features leading to a fully tunable structure. The role of the degree of nonequilibrium, temperature, and materials choice as well as features like noise, switching time, and current and power gain are also addressed.Comment: 8 pages, 9 figures, submitted to Journal of Low Temperature Physic

Tailoring Josephson coupling through superconductivity-induced nonequilibrium

The distinctive quasiparticle distribution existing under nonequilibrium in a superconductor-insulator-normal metal-insulator-superconductor (SINIS) mesoscopic line is proposed as a novel tool to control the supercurrent intensity in a long Josephson weak link. We present a description of this system in the framework of the diffusive-limit quasiclassical Green-function theory and take into account the effects of inelastic scattering with arbitrary strength. Supercurrent enhancement and suppression, including a marked transition to a $\pi$-junction are striking features leading to a fully tunable structure.Comment: 4 pages, 4 figure

Adiabatic pumping in a Superconductor-Normal-Superconductor weak link

We present a formalism to study adiabatic pumping through a superconductor - normal - superconductor weak link. At zero temperature, the pumped charge is related to the Berry phase accumulated, in a pumping cycle, by the Andreev bound states. We analyze in detail the case when the normal region is short compared to the superconducting coherence length. The pumped charge turns out to be an even function of the superconducting phase difference. Hence, it can be distinguished from the charge transferred due to the standard Josephson effect.Comment: 4 pages, 2 figures; Fig. 2 replaced, minor changes in the tex

Local density of states in metal - topological superconductor hybrid systems

We study by means of the recursive Green's function technique the local density-of-states of (finite and semi-infinite) multi-band spin-orbit coupled semiconducting nanowires in proximity to an s-wave superconductor and attached to normal-metal electrodes. When the nanowire is coupled to a normal electrode, the zero-energy peak, corresponding to the Majorana state in the topological phase, broadens with increasing transmission between the wire and the leads, eventually disappearing for ideal interfaces. Interestingly, for a finite transmission a peak is present also in the normal electrode, even though it has a smaller amplitude and broadens more rapidly with the strength of the coupling. Unpaired Majorana states can survive close to a topological phase transition even when the number of open channels (defined in the absence of superconductivity) is even. We finally study the Andreev-bound-state spectrum in superconductor-normal metal-superconductor junctions and find that in multi-band nanowires the distinction between topologically trivial and non-trivial systems based on the number of zero-energy crossings is preserved.Comment: 11 pages, 12 figures, published versio

Entanglement detection for electrons via witness operators

We discuss an implementation of the entanglement witness, a method to detect entanglement with few local measurements, in systems where entangled electrons are generated both in the spin and orbital degrees of freedom. We address the efficiency of this method in various setups, including two different particle-hole entanglement structures, and we demonstrate that it can also be used to infer information on the possible dephasing afflicting the devices.Comment: 12 pages, 5 figures; published versio

Cooling electrons by magnetic-field tuning of Andreev reflection

A solid-state cooling principle based on magnetic-field-driven tunable suppression of Andreev reflection in superconductor/two-dimensional electron gas nanostructures is proposed. This cooling mechanism can lead to very large heat fluxes per channel up to 10^4 times greater than currently achieved with superconducting tunnel junctions. This efficacy and its availability in a two-dimensional electron system make this method of particular relevance for the implementation of quantum nanostructures operating at cryogenic temperatures.Comment: 4 pages, 4 figures, published versio

Electronic Hong-Ou-Mandel interferometer for multi-mode entanglement detection

We show that multi-mode entanglement of electrons in a mesoscopic conductor can be detected by a measurement of the zero-frequency current correlations in an electronic Hong-Ou-Mandel interferometer. By this mean, one can further establish a lower bound to the entanglement of formation of two-electron input states. Our results extend the work of Burkard and Loss [Phys. Rev. Lett. 91, 087903 (2003)] to many channels and provide a way to test the existence of entangled states involving both orbital and spin degrees of freedom.Comment: 6 pages. Revised version. Ref. adde