Filling-Enforced Quantum Band Insulators in Spin-Orbit Coupled Crystals

While band insulators are usually described in wavevector space in terms of fully filled bands, they are sometimes also described in terms of a complementary Wannier picture in which electrons occupy localized, atom-like orbitals. Under what conditions does the latter picture break down? The presence of irremovable quantum entanglement between different sites can obstruct a localized orbital description, which occurs in systems like Chern and topological insulators. We collectively refer to such states as Quantum Band Insulators (QBIs). Here we report the theoretical discovery of a filling-enforced QBI - that is, a free electron insulator in which the band filling is smaller than the minimum number dictated by the atomic picture. Consequently such insulators have no representation in terms of filling localized orbitals and must be QBIs. This is shown to occur in models of certain cubic crystals with non-symmorphic space groups. Like topological insulators, filling-enforced QBIs require spin-orbit coupling. However, in contrast, they do not typically exhibit protected surface states. Instead their nontrivial nature is revealed by studying the quantum entanglement of their ground state wavefunction.Comment: 4.5 pages + 7.5 page Appendices, 2+4 figures; v3: Corrected Fig. 5 in Appendix B; added discussion on surface states (Fig. 6

Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals

We determine conditions on the filling of electrons in a crystalline lattice to obtain the equivalent of a band insulator -- a gapped insulator with neither symmetry breaking nor fractionalized excitations. We allow for strong interactions, which precludes a free particle description. Previous approaches that extend the Lieb-Schultz-Mattis argument invoked spin conservation in an essential way, and cannot be applied to the physically interesting case of spin-orbit coupled systems. Here we introduce two approaches, the first an entanglement based scheme, while the second studies the system on an appropriate flat `Bieberbach' manifold to obtain the filling conditions for all 230 space groups. These approaches only assume time reversal rather than spin rotation invariance. The results depend crucially on whether the crystal symmetry is symmorphic. Our results clarify when one may infer the existence of an exotic ground state based on the absence of order, and we point out applications to experimentally realized materials. Extensions to new situations involving purely spin models are also mentioned.Comment: 9 pages + 5 page appendices, 4 figures, 2 tables; v4: a typo in Figure 4 is correcte

Secondary periodicities of microbursts of TeV gamma rays from the Crab pulsar

Observations were made during the past several years on the Crab pulsar using the Ooty atmospheric Cerenkov array with the aim of detecting possible emission of ultra high energy gamma rays by the pulsar. During the course of these observations, it was found that the Crab pulsar emits TeV gamma rays in bursts of short duration. The microbursts of TeV gamma rays from the Crab pulsar, which were seen in the data of at least three years, also reveal interesting secondary periodicities. It was noticed at first that some bursts could be connected with the others that occurred during the same night or during the next two nights with integral number of cycles of periods 43 + or - 1 minute. Ten possible periods in the vicinity of 43 minutes were determined for all the combinations of bursts for each year. The best values of periods thus obtained were different from year to year. But when, instead of the real time, the number of Crab cycles elapsed between the bursts was used as the unit of time, two values of burst periods - 77460 and 77770 Crab cycles - were found to be significant in the data of at least two years. A Monte Carlo simulation using 1500 trial periods chosen randomly within + or - 5 minutes of the original burst period did not reveal any value of the period as significant

Predicting Combinatorial Binding of Transcription Factors to Regulatory Elements in the Human Genome by Association Rule Mining

Cis-acting transcriptional regulatory elements in mammalian genomes typically contain specific combinations of binding sites for various transcription factors. Although some cisregulatory elements have been well studied, the combinations of transcription factors that regulate normal expression levels for the vast majority of the 20,000 genes in the human genome are unknown. We hypothesized that it should be possible to discover transcription factor combinations that regulate gene expression in concert by identifying over-represented combinations of sequence motifs that occur together in the genome. In order to detect combinations of transcription factor binding motifs, we developed a data mining approach based on the use of association rules, which are typically used in market basket analysis. We scored each segment of the genome for the presence or absence of each of 83 transcription factor binding motifs, then used association rule mining algorithms to mine this dataset, thus identifying frequently occurring pairs of distinct motifs within a segment. Results: Support for most pairs of transcription factor binding motifs was highly correlated across different chromosomes although pair significance varied. Known true positive motif pairs showed higher association rule support, confidence, and significance than background. Our subsets of high-confidence, high-significance mined pairs of transcription factors showed enrichment for co-citation in PubMed abstracts relative to all pairs, and the predicted associations were often readily verifiable in the literature. Conclusion: Functional elements in the genome where transcription factors bind to regulate expression in a combinatorial manner are more likely to be predicted by identifying statistically and biologically significant combinations of transcription factor binding motifs than by simply scanning the genome for the occurrence of binding sites for a single transcription factor.NIAAA Alcohol Training GrantNational Science FoundationCellular and Molecular Biolog