Finite-size effects in a nanowire strongly coupled to a thin superconducting shell

We study the proximity effect in a one-dimensional nanowire strongly coupled to a finite superconductor with a characteristic size which is much shorter than its coherence length. Such geometries have become increasingly relevant in recent years in the experimental search for Majorana fermions with the development of thin epitaxial Al shells which form a very strong contact with either InAs or InSb nanowires. So far, however, no theoretical treatment of the proximity effect in these systems has accounted for the finite size of the superconducting film. We show that the finite-size effects become very detrimental when the level spacing of the superconductor greatly exceeds its energy gap. Without any fine-tuning of the size of the superconductor (on the scale of the Fermi wavelength), the tunneling energy scale must be larger than the level spacing in order to reach the hard gap regime which is seen ubiquitously in the experiments. However, in this regime, the large tunneling energy scale induces a large shift in the effective chemical potential of the nanowire and pushes the topological phase transition to magnetic field strengths which exceed the critical field of Al.Comment: 14 pages, 9 figure

Hard gap in a normal layer coupled to a superconductor

The ability to induce a sizable gap in the excitation spectrum of a normal layer placed in contact with a conventional superconductor has become increasingly important in recent years in the context of engineering a topological superconductor. The quasiclassical theory of the proximity effect shows that Andreev reflection at the superconductor/normal interface induces a nonzero pairing amplitude in the metal but does not endow it with a gap. Conversely, when the normal layer is atomically thin, the tunneling of Cooper pairs induces an excitation gap that can be as large as the bulk gap of the superconductor. We study how these two seemingly different views of the proximity effect evolve into one another as the thickness of the normal layer is changed. We show that a fully quantum-mechanical treatment of the problem predicts that the induced gap is always finite but falls off with the thickness of the normal layer, $d$. If $d$ is less than a certain crossover scale, which is much larger than the Fermi wavelength, the induced gap is comparable to the bulk gap. As a result, a sizable excitation gap can be induced in normal layers that are much thicker than the Fermi wavelength.Comment: 5 pages, 5 figures + 5 pages, 1 figure Supplementary Materia

AMIRIS - Agent based model for the integration of renewables into the electricity markets

The model AMIRIS allows the evaluation of political instruments and promotion mechanisms regarding their impact on actors‘ behaviours and development of the energy system. Actually the focus is set to energy economic changes due to the revised EGG 2012 and new possibilities of direct marketing of renewable electricity by § 33g (Marketpremium - MP), § 39 (Green electricity privilege) and local and regional direct marketing. Agents representing political framework, plant operators, intermediaries energy exchange market and distribution service operator are implemented in the model. Characteristics of the agents are based on beforehand performed analysis of actors. The poster shows the setup, simulation process and outcome of the AMIRIS model

Braucht ein neues Design: Der Strommarkt der Zukunft

Die Zukunft des Strommarktes wird im Bundesministerium für Wirtschaft und Energie derzeit diskutiert, im Sommer will Wirtschaftsminister Sigmar Gabriel mit der Vorlage des Weißbuches die Weichen für den Gesetzgebungsprozess Ende des Jahres stellen. Kann nur ein Kapazitätsmarkt Versorgungssicherheit bieten oder vermag das auch ein „Energy-Only- Markt 2.0 “ mit ergänzenden Maßnahmen? Wie können die richtigen Signale gesetzt werden, dass Deutschland seine Ziele beim Senken des Kohlendioxidausstoßes erreicht? Matthias Reeg Energiesystemanalytiker im DLR-Institut für Technische Thermodynamik hat das Projekt „Kapazitätsmechanismen als Rettungsschirm der Energiewende?“ im DLR geleitet und beschreibt im Interview mit DLR-Energieredakteurin Dorothee Bürkle, welche Möglichkeiten es gibt, den Strommarkt der Zukunft zu gestalten

Destructive interference of direct and crossed Andreev pairing in a system of two nanowires coupled via an s-wave superconductor

We consider a system of two one-dimensional nanowires coupled via an s-wave superconducting strip, a geometry that is capable of supporting Kramers pairs of Majorana fermions. By performing an exact analytical diagonalization of a tunneling Hamiltonian describing the proximity effect (via a Bogoliubov transformation), we show that the excitation gap of the system varies periodically on the scale of the Fermi wavelength in the limit where the interwire separation is shorter than the superconducting coherence length. Comparing with the excitation gaps in similar geometries containing only direct pairing, where one wire is decoupled from the superconductor, or only crossed Andreev pairing, where each nanowire is considered as a spin-polarized edge of a quantum Hall state, we find that the gap is always reduced, by orders of magnitude in certain cases, when both types of pairing are present. Our analytical results are further supported by numerical calculations on a tight-binding lattice. Finally, we show that treating the proximity effect by integrating out the superconductor using the bulk Green`s function does not reproduce the results of our exact diagonalization

Zero-energy Andreev bound states from quantum dots in proximitized Rashba nanowires

We study an analytical model of a Rashba nanowire that is partially covered by and coupled to a thin superconducting layer, where the uncovered region of the nanowire forms a quantum dot. We find that, even if there is no topological superconducting phase possible, there is a trivial Andreev bound state that becomes pinned exponentially close to zero energy as a function of magnetic field strength when the length of the quantum dot is tuned with respect to its spin-orbit length such that a resonance condition of Fabry-Perot type is satisfied. In this case, we find that the Andreev bound state remains pinned near zero energy for Zeeman energies that exceed the characteristic spacing between Andreev bound state levels but that are smaller than the spin-orbit energy of the quantum dot. Importantly, as the pinning of the Andreev bound state depends only on properties of the quantum dot, we conclude that this behavior is unrelated to topological superconductivity. To support our analytical model, we also perform a numerical simulation of a hybrid system while explicitly incorporating a thin superconducting layer, showing that all qualitative features of our analytical model are also present in the numerical results.Comment: Accepted for publication in Phys. Rev.

DIII topological superconductivity with emergent time-reversal symmetry

We find a class of topological superconductors which possess an emergent time-reversal symmetry that is present only after projecting to an effective low-dimensional model. We show that a topological phase in symmetry class DIII can be realized in a noninteracting system coupled to an s-wave superconductor only if the physical time-reversal symmetry of the system is broken, and we provide three general criteria that must be satisfied in order to have such a phase. We also provide an explicit model which realizes the class DIII topological superconductor in 1D. We show that, just as in time-reversal invariant topological superconductors, the topological phase is characterized by a Kramers pair of Majorana fermions that are protected by the emergent time-reversal symmetry

Low-field Topological Threshold in Majorana Double Nanowires

A hard proximity-induced superconducting gap has recently been observed in semiconductor nanowire systems at low magnetic fields. However, in the topological regime at high magnetic fields, a soft gap emerges and represents a fundamental obstacle to topologically protected quantum information processing with Majorana bound states. Here we show that in a setup of double Rashba nanowires that are coupled to an s-wave superconductor and subjected to an external magnetic field along the wires, the topological threshold can be significantly reduced by the destructive interference of direct and crossed-Andreev pairing in this setup, precisely down to the magnetic field regime in which current experimental technology allows for a hard superconducting gap. We also show that the resulting Majorana bound states exhibit sufficiently short localization lengths, which makes them ideal candidates for future braiding experiments