Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry

We present a general methodology towards the systematic characterization of crystalline topological insulating phases with time reversal symmetry (TRS).~In particular, taking the two-dimensional spinful hexagonal lattice as a proof of principle we study windings of Wilson loop spectra over cuts in the Brillouin zone that are dictated by the underlying lattice symmetries.~Our approach finds a prominent use in elucidating and quantifying the recently proposed ``topological quantum chemistry" (TQC) concept.~Namely, we prove that the split of an elementary band representation (EBR) by a band gap must lead to a topological phase.~For this we first show that in addition to the Fu-Kane-Mele $\mathbb{Z}_2$ classification, there is $C_2\mathcal{T}$-symmetry protected $\mathbb{Z}$ classification of two-band subspaces that is obstructed by the other crystalline symmetries, i.e.~forbidding the trivial phase. This accounts for all nontrivial Wilson loop windings of split EBRs \textit{that are independent of the parameterization of the flow of Wilson loops}.~Then, we show that while Wilson loop winding of split EBRs can unwind when embedded in higher-dimensional band space, two-band subspaces that remain separated by a band gap from the other bands conserve their Wilson loop winding, hence revealing that split EBRs are at least "stably trivial", i.e. necessarily non-trivial in the non-stable (few-band) limit but possibly trivial in the stable (many-band) limit.~This clarifies the nature of \textit{fragile} topology that has appeared very recently.~We then argue that in the many-band limit the stable Wilson loop winding is only determined by the Fu-Kane-Mele $\mathbb{Z}_2$ invariant implying that further stable topological phases must belong to the class of higher-order topological insulators.Comment: 27 pages, 13 figures, v2: minor corrections, new references included, v3: metastable topology of split EBRs emphasized, v4: prepared for publicatio

The space group classification of topological band insulators

Topological band insulators (TBIs) are bulk insulating materials which feature topologically protected metallic states on their boundary. The existing classification departs from time-reversal symmetry, but the role of the crystal lattice symmetries in the physics of these topological states remained elusive. Here we provide the classification of TBIs protected not only by time-reversal, but also by crystalline symmetries. We find three broad classes of topological states: (a) Gamma-states robust against general time-reversal invariant perturbations; (b) Translationally-active states protected from elastic scattering, but susceptible to topological crystalline disorder; (c) Valley topological insulators sensitive to the effects of non-topological and crystalline disorder. These three classes give rise to 18 different two-dimensional, and, at least 70 three-dimensional TBIs, opening up a route for the systematic search for new types of TBIs.Comment: Accepted in Nature Physic

Associations of common breast cancer susceptibility alleles with risk of breast cancer subtypes in BRCA1 and BRCA2 mutation carriers

Peer reviewedPublisher PD

Fat Mass and Obesity-Associated Gene (FTO) in Eating Disorders: Evidence for Association of the rs9939609 Obesity Risk Allele with Bulimia nervosa and Anorexia nervosa

Objective: The common single nucleotide polymorphism (SNP) rs9939609 in the fat mass and obesity-associated gene (FTO) is associated with obesity. As genetic variants associated with weight regulation might also be implicated in the etiology of eating disorders, we evaluated whether SNP rs9939609 is associated with bulimia nervosa (BN) and anorexia nervosa (AN). Methods: Association of rs9939609 with BN and AN was assessed in 689 patients with AN, 477 patients with BN, 984 healthy non-population-based controls, and 3,951 population-based controls (KORA-S4). Based on the familial and premorbid occurrence of obesity in patients with BN, we hypothesized an association of the obesity risk A-allele with BN. Results: In accordance with our hypothesis, we observed evidence for association of the rs9939609 A-allele with BN when compared to the non-population-based controls (unadjusted odds ratio (OR) = 1.142, one-sided 95% confidence interval (CI) 1.001-infinity; one-sided p = 0.049) and a trend in the population-based controls (OR = 1.124, one-sided 95% CI 0.932-infinity; one-sided p = 0.056). Interestingly, compared to both control groups, we further detected a nominal association of the rs9939609 A-allele to AN (OR = 1.181, 95% CI 1.027-1.359, two-sided p = 0.020 or OR = 1.673, 95% CI 1.101-2.541, two-sided p = 0.015,). Conclusion: Our data suggest that the obesity-predisposing FTO allele might be relevant in both AN and BN. Copyright (C) 2012 S. Karger GmbH, Freibur

In vivo validation of an experimental adaptive quantitative coronary angiography algorithm to circumvent overestimation of small luminal diameters

The reliability of quantitative coronary angiography (QCA) measurements is of fundamental importance for the study and practice of interventional cardiology. In vivo validation results have consistently reported a tendency for QCA systems to overestimate small luminal diameters. Such a systematic error may result in the underestimation of luminal gain during intracoronary procedures and in the underestimation of progression of coronary artery disease during longitudinal studies. We report the in vivo validation results of an experimental adaptive edge‐detection algorithm that was developed to reduce overestimation of small luminal diameters by incorporating a dynamic function of variable kernel size of the derivative operator and variable weighting of the first and second derivatives of the brightness profile. The results of the experimental algorithm were compared to those of the conventional parent edge detection algorithm with fixed parameters. Dynamic adjustment of the edge‐detection algorithm parameters was found to improve measurements of small (lt;0.8‐mm) luminal diameters as evidenced by an intercept of +.07 mm for the algorithm with variable weighting compared to +0.21 mm for the parent algorithm with fixed weighting. A slope of <1 was found for both the parent and experimental algorithms with subsequent underestimation of large luminal diameters. S

BRCA2 polymorphic stop codon K3326X and the risk of breast, prostate, and ovarian cancers

Background: The K3326X variant in BRCA2 (BRCA2*c.9976A&gt;T; p.Lys3326*; rs11571833) has been found to be associated with small increased risks of breast cancer. However, it is not clear to what extent linkage disequilibrium with fully pathogenic mutations might account for this association. There is scant information about the effect of K3326X in other hormone-related cancers. Methods: Using weighted logistic regression, we analyzed data from the large iCOGS study including 76 637 cancer case patients and 83 796 control patients to estimate odds ratios (ORw) and 95% confidence intervals (CIs) for K3326X variant carriers in relation to breast, ovarian, and prostate cancer risks, with weights defined as probability of not having a pathogenic BRCA2 variant. Using Cox proportional hazards modeling, we also examined the associations of K3326X with breast and ovarian cancer risks among 7183 BRCA1 variant carriers. All statistical tests were two-sided. Results: The K3326X variant was associated with breast (ORw = 1.28, 95% CI = 1.17 to 1.40, P = 5.9x10- 6) and invasive ovarian cancer (ORw = 1.26, 95% CI = 1.10 to 1.43, P = 3.8x10-3). These associations were stronger for serous ovarian cancer and for estrogen receptor–negative breast cancer (ORw = 1.46, 95% CI = 1.2 to 1.70, P = 3.4x10-5 and ORw = 1.50, 95% CI = 1.28 to 1.76, P = 4.1x10-5, respectively). For BRCA1 mutation carriers, there was a statistically significant inverse association of the K3326X variant with risk of ovarian cancer (HR = 0.43, 95% CI = 0.22 to 0.84, P = .013) but no association with breast cancer. No association with prostate cancer was observed. Conclusions: Our study provides evidence that the K3326X variant is associated with risk of developing breast and ovarian cancers independent of other pathogenic variants in BRCA2. Further studies are needed to determine the biological mechanism of action responsible for these associations