We present an implementation of G0W0 calculations including spin-orbit coupling (SOC) enabling investigations of large systems, with thousands of electrons, and we discuss results for molecules, solids, and nanocrystals. Using a newly developed set of molecules with heavy elements (called GW-SOC81), we find that, when based upon hybrid density functional calculations, fully relativistic (FR) and scalar-relativistic (SR) G0W0 calculations of vertical ionization potentials both yield excellent performance compared to experiment, with errors below 1.9%. We demonstrate that while SR calculations have higher random errors, FR calculations systematically underestimate the VIP by 0.1 to 0.2 eV. We further verify that SOC effects may be well approximated at the FR density functional level and then added to SR G0W0 results for a broad class of systems. We also address the use of different root-finding algorithms for the G0W0 quasiparticle equation and the significant influence of including d electrons in the valence partition of the pseudopotential for G0W0 calculations. Finally, we present statistical analyses of our data, highlighting the importance of separating definitive improvements from those that may occur by chance due to a limited number of samples. We suggest the statistical analyses used here will be useful in the assessment of the accuracy of a large variety of electronic structure methods.

We present numerical simulations of phase imprinting experiments in ultracold trapped Fermi gases which are in good agreement with recent, independent experimental results. Our focus is on the sequence and evolution of defects using the fermionic time-dependent Ginzburg-Landau equation, which contains dissipation necessary for equilibration. In contrast to other simulations we introduce small, experimentally unavoidable symmetry breaking, particularly that associated with thermal fluctuations and with the phase imprinting tilt angle, and illustrate their dramatic effects. The former causes vortex rings in confined geometries to move to the trap surface and rapidly decay into more stable vortex lines, as appears consistent with recent experimental claims. The latter aligns the precessing and relatively long-lived vortex filaments, rendering them difficult to distinguish from solitons.

Surface defects created and probed with scanning tunneling microscopes are a promising platform for atomic-scale electronics and quantum information technology applications. Using first-principles calculations we demonstrate how to engineer dangling bond (DB) defects on hydrogenated Si(100) surfaces, which give rise to isolated impurity states that can be used in atomic-scale devices. In particular we show that sample thickness and biaxial strain can serve as control parameters to design the electronic properties of DB defects. While in thick Si samples the neutral DB state is resonant with bulk valence bands, ultrathin samples (1-2 nm) lead to an isolated impurity state in the gap; similar behavior is seen for DB pairs and DB wires. Strain further isolates the DB from the valence band, with the response to strain heavily dependent on sample thickness. These findings suggest new methods for tuning the properties of defects on surfaces for electronic and quantum information applications. Finally, we present a consistent and unifying interpretation of many results presented in the literature for DB defects on hydrogenated silicon surfaces, rationalizing apparent discrepancies between different experiments and simulations. arXiv:1702.07747v2 [cond-mat.mtrl-sci]

We address the important question of how to characterize the normal state and the nature of noncondensed pairs in fermionic superfiuids under the influence of a strong effective magnetic field. In ultracold gases, the magnetic field is implemented through rapid rotation or novel artificial field techniques. We consider the near-unitary regime, where noncondensed pairs are likely to be present at temperatures above the condensation temperature Tc. We show (based on Gor'kov theory) that these pairs are associated with a precursor of a vortex configuration. Importantly, this nonuniform normal state appears to enable "Bose condensation" in a field which is otherwise problematic due to the effective one-dimensionality of Landau-level dispersion.

We address band engineering in the presence of periodic driving by numerically shaking a lattice containing a bosonic condensate. By not restricting to simplified band structure models we are able to address arbitrary values of the shaking frequency, amplitude, and interaction strengths g. For "near-resonant" shaking frequencies with moderate g, a quantum phase transition to a finite momentum superfluid is obtained with Kibble-Zurek scaling and quantitative agreement with experiment. We use this successful calibration as a platform to support a more general investigation of the interplay between (one particle) Floquet theory and the effects associated with arbitrary g. Band crossings lead to superfluid destabilization, but where this occurs depends on g in a complicated fashion.