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

Unnesting of Copatterns

Inductive data such as finite lists and trees can elegantly be defined by constructors which allow programmers to analyze and manipulate finite data via pattern matching. Dually, coinductive data such as streams can be defined by observations such as head and tail and programmers can synthesize infinite data via copattern matching. This leads to a symmetric language where finite and infinite data can be nested. In this paper, we compile nested pattern and copattern matching into a core language which only supports simple non-nested (co)pattern matching. This core language may serve as an intermediate language of a compiler. We show that this translation is conservative, i.e. the multi-step reduction relation in both languages coincides for terms of the original language. Furthermore, we show that the translation preserves strong and weak normalisation: a term of the original language is strongly/weakly normalising in one language if and only if it is so in the other. In the proof we develop more general criteria which guarantee that extensions of abstract reduction systems are conservative and preserve strong or weak normalisation. \ua9 2014 Springer International Publishing Switzerland

First-principles calculations of the Berry curvature of Bloch states for charge and spin transport of electrons

Recent progress in wave packet dynamics based on the insight of Berry pertaining to adiabatic evolution of quantum systems has led to the need for a new property of a Bloch state, the Berry curvature, to be calculated from first principles. We report here on the response to this challenge by the ab initio community during the past decade. First we give a tutorial introduction of the conceptual developments we mentioned above. Then we describe four methodologies which have been developed for first-principle calculations of the Berry curvature. Finally, to illustrate the significance of the new developments, we report some results of calculations of interesting physical properties such as the anomalous and spin Hall conductivity as well as the anomalous Nernst conductivity and discuss the influence of the Berry curvature on the de Haas–van Alphen oscillation

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

POPLMark reloaded: Mechanizing proofs by logical relations

We propose a new collection of benchmark problems in mechanizing the metatheory of programming languages, in order to compare and push the state of the art of proof assistants. In particular, we focus on proofs using logical relations (LRs) and propose establishing strong normalization of a simply typed calculus with a proof by Kripke-style LRs as a benchmark. We give a modern view of this well-understood problem by formulating our LR on well-typed terms. Using this case study, we share some of the lessons learned tackling this problem in different dependently typed proof environments. In particular, we consider the mechanization in Beluga, a proof environment that supports higher-order abstract syntax encodings and contrast it to the development and strategies used in general-purpose proof assistants such as Coq and Agda. The goal of this paper is to engage the community in discussions on what support in proof environments is needed to truly bring mechanized metatheory to the masses and engage said community in the crafting of future benchmarks

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

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

Time-resolved magnetophotoluminescence studies of magnetic polaron dynamics in type-II quantum dots

We used continuous wave photoluminescence (cw-PL) and time resolved photoluminescence (TR-PL) spectroscopy to compare the properties of magnetic polarons (MP) in two related spatially indirect II-VI epitaxially grown quantum dot systems. In the ZnTe/(Zn,Mn)Se system the holes are confined in the non-magnetic ZnTe quantum dots (QDs), and the electrons reside in the magnetic (Zn,Mn)Se matrix. On the other hand, in the (Zn,Mn)Te/ZnSe system, the holes are confined in the magnetic (Zn,Mn)Te QDs, while the electrons remain in the surrounding non-magnetic ZnSe matrix. The magnetic polaron formation energies in both systems were measured from the temporal red-shift of the band-edge emission. The magnetic polaron exhibits distinct characteristics depending on the location of the Mn ions. In the ZnTe/(Zn,Mn)Se system the magnetic polaron shows conventional behavior with decreasing with increasing temperature T and increasing magnetic field B. In contrast, in the (Zn,Mn)Te/ZnSe system has unconventional dependence on temperature T and magnetic field B; is weakly dependent on T as well as on B. We discuss a possible origin for such a striking difference in the MP properties in two closely related QD systems.Comment: 27 pages, 12 figure

Exploring the link between MORF4L1 and risk of breast cancer.

INTRODUCTION: Proteins encoded by Fanconi anemia (FA) and/or breast cancer (BrCa) susceptibility genes cooperate in a common DNA damage repair signaling pathway. To gain deeper insight into this pathway and its influence on cancer risk, we searched for novel components through protein physical interaction screens. METHODS: Protein physical interactions were screened using the yeast two-hybrid system. Co-affinity purifications and endogenous co-immunoprecipitation assays were performed to corroborate interactions. Biochemical and functional assays in human, mouse and Caenorhabditis elegans models were carried out to characterize pathway components. Thirteen FANCD2-monoubiquitinylation-positive FA cell lines excluded for genetic defects in the downstream pathway components and 300 familial BrCa patients negative for BRCA1/2 mutations were analyzed for genetic mutations. Common genetic variants were genotyped in 9,573 BRCA1/2 mutation carriers for associations with BrCa risk. RESULTS: A previously identified co-purifying protein with PALB2 was identified, MRG15 (MORF4L1 gene). Results in human, mouse and C. elegans models delineate molecular and functional relationships with BRCA2, PALB2, RAD51 and RPA1 that suggest a role for MRG15 in the repair of DNA double-strand breaks. Mrg15-deficient murine embryonic fibroblasts showed moderate sensitivity to γ-irradiation relative to controls and reduced formation of Rad51 nuclear foci. Examination of mutants of MRG15 and BRCA2 C. elegans orthologs revealed phenocopy by accumulation of RPA-1 (human RPA1) nuclear foci and aberrant chromosomal compactions in meiotic cells. However, no alterations or mutations were identified for MRG15/MORF4L1 in unclassified FA patients and BrCa familial cases. Finally, no significant associations between common MORF4L1 variants and BrCa risk for BRCA1 or BRCA2 mutation carriers were identified: rs7164529, Ptrend = 0.45 and 0.05, P2df = 0.51 and 0.14, respectively; and rs10519219, Ptrend = 0.92 and 0.72, P2df = 0.76 and 0.07, respectively. CONCLUSIONS: While the present study expands on the role of MRG15 in the control of genomic stability, weak associations cannot be ruled out for potential low-penetrance variants at MORF4L1 and BrCa risk among BRCA2 mutation carriers.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are