Superconductor Vortex Spectrum Including Fermi Arc States in Time-Reversal Symmetric Weyl Semimetals.

Using semiclassics to surmount the hurdle of bulk-surface inseparability, we derive the superconductor vortex spectrum in nonmagnetic Weyl semimetals and show that it stems from the Berry phase of orbits made of Fermi arcs on opposite surfaces and bulk chiral modes. Tilting the vortex transmutes it between bosonic, fermionic, and supersymmetric, produces periodic peaks in the density of states that signify novel nonlocal Majorana modes, and yields a thickness-independent spectrum at magic "magic angles." We propose (Nb,Ta)P as candidate materials and tunneling spectroscopy as the ideal experiment.

Fermi Arc Criterion for Surface Majorana Modes in Superconducting Time-Reversal Symmetric Weyl Semimetals.

Many clever routes to Majorana fermions have been discovered by exploiting the interplay between superconductivity and band topology in metals and insulators. However, realizations in semimetals remain less explored. We ask, "Under what conditions do superconductor vortices in time-reversal symmetric Weyl semimetals-three-dimensional semimetals with only time-reversal symmetry-trap Majorana fermions on the surface?" If each constant-k_{z} plane, where z is the vortex axis, contains equal numbers of Weyl nodes of each chirality, we predict a generically gapped vortex and derive a topological invariant ν=±1 in terms of the Fermi arc structure that signals the presence or absence of surface Majorana fermions.

Power-Law Temperature Dependence of the Penetration Depth in a Topological Superconductor Due to Surface States.

We study the temperature dependence of the magnetic penetration depth in a 3D topological superconductor (TSC), incorporating the paramagnetic current due to the surface states. A TSC is predicted to host a gapless 2D surface Majorana fluid. In addition to the bulk-dominated London response, we identify a T^{3} power-law-in-temperature contribution from the surface, valid in the low-temperature limit.

Time-reversal asymmetry without local moments via directional scalar spin chirality.

Invariably, time-reversal symmetry (TRS) violation in a state of matter is identified with static magnetism in it. Here, a directional scalar spin chiral order (DSSCO) phase is introduced that disobeys this basic principle: it breaks TRS but has no density of static moments. It can be obtained by melting the spin moments in a magnetically ordered phase but retaining residual broken TRS.

Erratum: Charge Transport in Weyl Semimetals [Phys. Rev. Lett. 108, 046602 (2012)].

This corrects the article DOI: 10.1103/PhysRevLett.108.

Possible transport evidence for three-dimensional topological superconductivity in doped β-PdBi.

Interest in topological states of matter burgeoned over a decade ago with the theoretical prediction and experimental detection of topological insulators, especially in bulk three-dimensional insulators that can be tuned out of it by doping. Their superconducting counterpart, the fully-gapped three-dimensional time-reversal-invariant topological superconductors, have evaded discovery in bulk intrinsic superconductors so far. The recently discovered topological metal β-PdBi is a unique candidate for tunable bulk topological superconductivity because of its intrinsic superconductivity and spin-orbit-coupling.

Characterizing eigenstate thermalization via measures in the Fock space of operators.

The eigenstate thermalization hypothesis (ETH) attempts to bridge the gap between quantum mechanical and statistical mechanical descriptions of isolated quantum systems. Here, we define unbiased measures for how well the ETH works in various regimes, by mapping general interacting quantum systems on regular lattices onto a single particle living on a high-dimensional graph. By numerically analyzing deviations from ETH behavior in the nonintegrable Ising model, we propose a quantity that we call the n-weight to democratically characterize the average deviations for all operators residing on a given number of sites, irrespective of their spatial structure.

Quantum oscillations from generic surface Fermi arcs and bulk chiral modes in Weyl semimetals.

We re-examine the question of quantum oscillations from surface Fermi arcs and chiral modes in Weyl semimetals. By introducing two tools--semiclassical phase-space quantization and a numerical implementation of a layered construction of Weyl semimetals--we discover several important generalizations to previous conclusions that were implicitly tailored to the special case of identical Fermi arcs on top and bottom surfaces. We show that the phase-space quantization picture fixes an ambiguity in the previously utilized energy-time quantization approach and correctly reproduces the numerically calculated quantum oscillations for generic Weyl semimetals with distinctly curved Fermi arcs on the two surfaces.

Charge transport in Weyl semimetals.

We study transport in Weyl semimetals with N isotropic Weyl nodes in the presence of Coulomb interactions or disorder at temperature T. In the interacting clean limit, we determine the conductivity σ(ω,T) by solving a quantum Boltzmann equation within a "leading log" approximation and find it to be proportional to T, up to logarithmic factors arising from the flow of couplings. In the noninteracting disordered case, we compute the Kubo conductivity and show that it behaves differently for ω << T and ω >> T: in the former regime we recover a previous result, of a finite dc conductivity and a Drude width vanishing as NT(2); in the latter, we find that σ(ω,T) vanishes linearly with ω with a leading term as T → 0 equal to the clean, free-fermion result: σ(0)((N))(ω,T = 0) = Ne(2)/12h|ω|/v(F).

Ultracold atoms in a tunable optical kagome lattice.

We realize a two-dimensional kagome lattice for ultracold atoms by overlaying two commensurate triangular optical lattices generated by light at the wavelengths of 532 and 1064 nm. Stabilizing and tuning the relative position of the two lattices, we explore different lattice geometries including a kagome, a one-dimensional stripe, and a decorated triangular lattice. We characterize these geometries using Kapitza-Dirac diffraction and by analyzing the Bloch-state composition of a superfluid released suddenly from the lattice.

Majorana modes at the ends of superconductor vortices in doped topological insulators.

Recent experiments have observed bulk superconductivity in doped topological insulators. Here we ask whether vortex Majorana zero modes, previously predicted to occur when s-wave superconductivity is induced on the surface of topological insulators, survive in these doped systems with metallic normal states. Assuming inversion symmetry, we find that they do but only below a critical doping.