In-situ strain tuning of the Dirac surface states in Bi2Se3 films

Elastic strain has the potential for a controlled manipulation of the band gap and spin-polarized Dirac states of topological materials, which can lead to pseudo-magnetic-field effects, helical flat bands and topological phase transitions. However, practical realization of these exotic phenomena is challenging and yet to be achieved. Here, we show that the Dirac surface states of the topological insulator Bi2Se3 can be reversibly tuned by an externally applied elastic strain. Performing in-situ x-ray diffraction and in-situ angle-resolved photoemission spectroscopy measurements during tensile testing of epitaxial Bi2Se3 films bonded onto a flexible substrate, we demonstrate elastic strains of up to 2.1% and quantify the resulting reversible changes in the topological surface state. Our study establishes the functional relationship between the lattice and electronic structures of Bi2Se3 and, more generally, demonstrates a new route toward momentum-resolved mapping of strain-induced band structure changes

Finding topological subgraphs is fixed-parameter tractable

We show that for every fixed undirected graph $H$, there is a $O(|V(G)|^3)$ time algorithm that tests, given a graph $G$, if $G$ contains $H$ as a topological subgraph (that is, a subdivision of $H$ is subgraph of $G$). This shows that topological subgraph testing is fixed-parameter tractable, resolving a longstanding open question of Downey and Fellows from 1992. As a corollary, for every $H$ we obtain an $O(|V(G)|^3)$ time algorithm that tests if there is an immersion of $H$ into a given graph $G$. This answers another open question raised by Downey and Fellows in 1992

Momentum space imaging of Cooper pairing in a half-Dirac-gas topological superconductor (a helical 2D topological superconductor)

Superconductivity in Dirac electrons has recently been proposed as a new platform between novel concepts in high-energy and condensed matter physics. It has been proposed that supersymmetry and exotic quasiparticles, both of which remain elusive in particle physics, may be realized as emergent particles in superconducting Dirac electron systems. Using artificially fabricated topological insulator-superconductor heterostructures, we present direct spectroscopic evidence for the existence of Cooper pairing in a half Dirac gas 2D topological superconductor. Our studies reveal that superconductivity in a helical Dirac gas is distinctly different from that of in an ordinary two-dimensional superconductor while considering the spin degrees of freedom of electrons. We further show that the pairing of Dirac electrons can be suppressed by time-reversal symmetry breaking impurities removing the distinction. Our demonstration and momentum-space imaging of Cooper pairing in a half Dirac gas and its magnetic behavior taken together serve as a critically important 2D topological superconductor platform for future testing of novel fundamental physics predictions such as emergent supersymmetry and quantum criticality in topological systems.Comment: Submitted June'14; Accepted to NaturePhysics, to appear AOP (2014

Multiple testing with persistent homology

Multiple hypothesis testing requires a control procedure. Simply increasing simulations or permutations to meet a Bonferroni-style threshold is prohibitively expensive. In this paper we propose a null model based approach to testing for acyclicity, coupled with a Family-Wise Error Rate (FWER) control method that does not suffer from these computational costs. We adapt an False Discovery Rate (FDR) control approach to the topological setting, and show it to be compatible both with our null model approach and with previous approaches to hypothesis testing in persistent homology. By extending a limit theorem for persistent homology on samples from point processes, we provide theoretical validation for our FWER and FDR control methods