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

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.

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

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

Metallization of Rashba wire by superconducting layer in the strong-proximity regime

Semiconducting quantum wires defined within two-dimensional electron gases and strongly coupled to thin superconducting layers have been extensively explored in recent experiments as promising platforms to host Majorana bound states. We study numerically such a geometry, consisting of a quasi-one-dimensional wire coupled to a disordered three-dimensional superconducting layer. We find that, in the strong-coupling limit of a sizable proximity-induced superconducting gap, all transverse subbands of the wire are significantly shifted in energy relative to the chemical potential of the wire. For the lowest subband, this band shift is comparable in magnitude to the spacing between quantized levels that arise due to the finite thickness of the superconductor (which typically is $\sim500$ meV for a 10-nm-thick layer of Aluminum); in higher subbands, the band shift is much larger. Additionally, we show that the width of the system, which is usually much larger than the thickness, and moderate disorder within the superconductor have almost no impact on the induced gap or band shift. We provide a detailed discussion of the ramifications of our results, arguing that a huge band shift and significant renormalization of semiconducting material parameters in the strong-coupling limit make it challenging to realize a topological phase in such a setup, as the strong coupling to the superconductor essentially metallizes the semiconductor. This metallization of the semiconductor can be tested experimentally through the measurement of the band shift.Comment: 11 pages, 12 figures, version accepted to Phys. Rev.

Proximity effect in a two-dimensional electron gas coupled to a thin superconducting layer

There have recently been several experiments studying induced superconductivity in semiconducting two-dimensional electron gases that are strongly coupled to thin superconducting layers, as well as probing possible topological phases supporting Majorana bound states in such setups. We show that a large band shift is induced in the semiconductor by the superconductor in this geometry, thus making it challenging to realize a topological phase. Additionally, we show that while increasing the thickness of the superconducting layer reduces the magnitude of the band shift, it also leads to a more significant renormalization of the semiconducting material parameters and does not reduce the challenge of tuning into a topological phase.Comment: Appearing in Beilstein Journal of Nanotechnology thematic series on "Topological Materials

Innovation Influences Liking for Chocolates Among Neophilic Consumers

The fear of trying new foods is a major barrier for entry for innovative ingredients, foods, flavors, or cuisines into the market place. We explored the relationship between perceived innovation and liking for chocolates and degree of neophobia. Line scales were used to measure: innovation, liking, and perceived dollar value for three chocolate confections. One was a traditional confection (palette d′or), and two others were designed to be more innovative (white miso with dark chocolate and white chocolate with candied black olive). An analysis of variance found that panelists (n=44) perceived significant (p\u3c0.01) differences among the chocolates in innovation, and liking, but not dollar value or estimated caloric content. The chocolate rated as the most innovative was also rated as the least liked. This finding is significant since the mean neophobia score of our subjects was quite low and very few of them would have been classified as neophobic. This current work suggests that acceptance of innovative new foods is dependent, in part, upon factors that transcend neophobic mindsets. Chefs and product developers should be aware of the fact that even among neophilic consumers who are quite willing to consume novel foods, there is a possibility that a food might be too innovative, resulting in a negative impact on liking

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

Limited rigor in studies of raptor mortality and mitigation at wind power facilities

Wind power is an expanding source of renewable energy. However, there are ecological challenges related to wind energy generation, including collisions of wildlife with turbines. Lack of rigor, and variation in study design, together limit efforts to understand the broad-scale effects of wind power infrastructure on wildlife populations. It is not clear, however, whether these types of limitations apply to groups of birds such as raptors that are particularly vulnerable to negative effects of wind energy. We reviewed 672 peer-reviewed publications, unpublished reports, and citations from 321 wind facilities in 12 countries to evaluate methods used to monitor and mitigate for wind facility impacts on raptors. Most reports that included raptor monitoring (86 %, n = 461) only conducted post-construction monitoring for raptor fatalities, while few (12 %; n = 65) estimated preconstruction raptor use. Only 27 % of facilities (n = 62) provided estimates of fatalities or raptor use across multiple construction phases, and the percentage of facilities with data available from multiple construction periods has not changed over time. A formal experimental study design was incorporated into surveys at only 29 % of facilities. Finally, mitigation practices to reduce impacts on raptors were only reported at 23 % of facilities. Our results suggest that rigorous data collection on wind energy impacts to raptors is rare, and that mitigation of detrimental effects is seldom reported. Expanding the use of rigorous research approaches and increasing data availability would improve understanding of the regional and global effects of wind energy on raptor populations

`imaka - a ground-layer adaptive optics system on Maunakea

We present the integration status for `imaka, the ground-layer adaptive optics (GLAO) system on the University of Hawaii 2.2-meter telescope on Maunakea, Hawaii. This wide-field GLAO pathfinder system exploits Maunakea's highly confined ground layer and weak free-atmosphere to push the corrected field of view to ~1/3 of a degree, an areal field approaching an order of magnitude larger than any existing or planned GLAO system, with a FWHM ~ 0.33 arcseconds in the visible and near infrared. We discuss the unique design aspects of the instrument, the driving science cases and how they impact the system, and how we will demonstrate these cases on the sky.Comment: 9 pages, 5 figure