Topological superconductivity in proximity to type-II superconductors

One-dimensional systems proximity coupled to a superconductor can be driven into a topological superconducting phase by an external magnetic field. Here, we investigate the effect of vortices created by the magnetic field in a type-II superconductor providing the proximity effect. We identify different ways in which the topological protection of Majorana modes can be compromised and discuss strategies to circumvent these detrimental effects. Our findings are also relevant to topological phases of proximitized quantum Hall edge states

On calculating the Berry curvature of Bloch electrons using the KKR method

We propose and implement a particularly effective method for calculating the Berry curvature arising from adiabatic evolution of Bloch states in wave vector k space. The method exploits a unique feature of the Korringa-Kohn-Rostoker (KKR) approach to solve the Schr\"odinger or Dirac equations. Namely, it is based on the observation that in the KKR method k enters the calculation via the structure constants which depend only on the geometry of the lattice but not the crystal potential. For both the Abelian and non-Abelian Berry curvature we derive an analytic formula whose evaluation does not require any numerical differentiation with respect to k. We present explicit calculations for Al, Cu, Au, and Pt bulk crystals.Comment: 13 pages, 5 figure

Topological superconductivity in a phase-controlled Josephson junction

Topological superconductors can support localized Majorana states at their boundaries(1-5). These quasi-particle excitations obey non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner(6,7). Although signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scaled to large numbers of states(8-21). Here we present an experimental approach towards a two-dimensional architecture of Majorana bound states. Using a Josephson junction made of a HgTe quantum well coupled to thin-film aluminium, we are able to tune the transition between a trivial and a topological superconducting state by controlling the phase difference across the junction and applying an in-plane magnetic field(22). We determine the topological state of the resulting superconductor by measuring the tunnelling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunnelling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunnelling conductance develops a zero-bias peak, which persists over a range of phase differences that expands systematically with increasing magnetic field. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and probing topological superconducting phases in two-dimensional systems

First Physics Results at the Physical Pion Mass from Nf=2N_f = 2 Wilson Twisted Mass Fermions at Maximal Twist

We present physics results from simulations of QCD using $N_f = 2$ dynamical Wilson twisted mass fermions at the physical value of the pion mass. These simulations were enabled by the addition of the clover term to the twisted mass quark action. We show evidence that compared to previous simulations without this term, the pion mass splitting due to isospin breaking is almost completely eliminated. Using this new action, we compute the masses and decay constants of pseudoscalar mesons involving the dynamical up and down as well as valence strange and charm quarks at one value of the lattice spacing, $a \approx 0.09$ fm. Further, we determine renormalized quark masses as well as their scale-independent ratios, in excellent agreement with other lattice determinations in the continuum limit. In the baryon sector, we show that the nucleon mass is compatible with its physical value and that the masses of the $\Delta$ baryons do not show any sign of isospin breaking. Finally, we compute the electron, muon and tau lepton anomalous magnetic moments and show the results to be consistent with extrapolations of older ETMC data to the continuum and physical pion mass limits. We mostly find remarkably good agreement with phenomenology, even though we cannot take the continuum and thermodynamic limits.Comment: 45 pages, 15 figure

Zero-voltage conductance peak from weak antilocalization in a Majorana nanowire

We show that weak antilocalization by disorder competes with resonant Andreev reflection from a Majorana zero-mode to produce a zero-voltage conductance peak of order e^2/h in a superconducting nanowire. The phase conjugation needed for quantum interference to survive a disorder average is provided by particle-hole symmetry - in the absence of time-reversal symmetry and without requiring a topologically nontrivial phase. We identify methods to distinguish the Majorana resonance from the weak antilocalization effect.Comment: 13 pages, 8 figures. Addendum, February 2014: Appendix B shows results for weak antilocalization in the circular ensemble. (This appendix is not in the published version.

Needle & knot : binder boilerplate tied up

To lighten the burden of programming language mechanization, many approaches have been developed that tackle the substantial boilerplate which arises from variable binders. Unfortunately, the existing approaches are limited in scope. They typically do not support complex binding forms (such as multi-binders) that arise in more advanced languages, or they do not tackle the boilerplate due to mentioning variables and binders in relations. As a consequence, the human mechanizer is still unnecessarily burdened with binder boilerplate and discouraged from taking on richer languages. This paper presents Knot, a new approach that substantially extends the support for binder boilerplate. Knot is a highly expressive language for natural and concise specification of syntax with binders. Its meta-theory constructively guarantees the coverage of a considerable amount of binder boilerplate for well-formed specifications, including that for well-scoping of terms and context lookups. Knot also comes with a code generator, Needle, that specializes the generic boilerplate for convenient embedding in COQ and provides a tactic library for automatically discharging proof obligations that frequently come up in proofs of weakening and substitution lemmas of type-systems. Our evaluation shows, that Needle & Knot significantly reduce the size of language mechanizations (by 40% in our case study). Moreover, as far as we know, Knot enables the most concise mechanization of the POPLmark Challenge (1a + 2a) and is two-thirds the size of the next smallest. Finally, Knot allows us to mechanize for instance dependentlytyped languages, which is notoriously challenging because of dependent contexts and mutually-recursive sorts with variables

Association of polymorphisms in CYP19A1 and CYP3A4 genes with lower urinary tract symptoms, prostate volume, uroflow and PSA in a population-based sample

PURPOSE: The known importance of testosterone for the development of benign prostatic hyperplasia (BPH) prompted us to test the hypothesis whether polymorphisms of two genes (CYP19A1 and CYP3A4) involved in testosterone metabolism are associated with clinical BPH-parameters. METHODS: A random sample of the population-based Herne lower urinary tract symptoms cohort was analysed. All these men underwent a detailed urological work-up. Two polymorphisms in the CYP19A1 gene [rs700518 in exon 4 (A57G); rs10046 at the 3'UTR(C268T)] and one in the 3'UTR of CYP3A4 [rs2740574 (A392G)] were determined by TaqMan assay from genomic DNA of peripheral blood. These polymorphisms were correlated to clinical and laboratory BPH-parameters. RESULTS: A total of 392 men (65.4 +/- 7.0 years; 52-79 years) were analysed. Mean International Prostate Symptom Score (IPSS; 7.5), Q (max) (15.4 ml/s), prostate volume (31 ml) and prostate specific antigen (PSA) (1.8 ng/ml) indicated a typical elderly population. Both polymorphisms in the CYP19A1 gene were not correlated to age, IPSS, Q (max), prostate volume and post-void residual volume. Serum PSA was higher in men carrying the heterozygous rs10046 genotype (2.0 +/- 0.1 ng/ml) than in those with the CC-genotype (1.7 +/- 0.2 ng/ml, P = 0.012). Men carrying one a mutated allele of the CYP3A4 gene had smaller prostates (27.0 +/- 2.0 vs. 32 +/- 0.8 ml, P = 0.02) and lower PSA levels (1.6 +/- 0.3 vs. 1.9 +/- 0.1 ng/ml). CONCLUSIONS: The inconsistent associations observed herein and for other gene polymorphisms warrant further studies. In general, the data regarding the association of gene polymorphism to BPH-parameters suggest that this disease is caused by multiple rather than a single genetic variant. A rigorous patient selection based on anatomo-pathological and hormonal profile may possible reduce the number of confounders for future studies thus enabling a more detailed assessment of the association between genetic factors and BPH-parameter