William S. Cole

Bose-Hubbard models with synthetic spin-orbit coupling: Mott insulators, spin textures, and superfluidity.

Motivated by the experimental realization of synthetic spin-orbit coupling for ultracold atoms, we investigate the phase diagram of the Bose-Hubbard model in a non-Abelian gauge field in two dimensions. Using a strong coupling expansion in the combined presence of spin-orbit coupling and tunable interactions, we find a variety of interesting magnetic Hamiltonians in the Mott insulator (MI), which support magnetic textures such as spin spirals and vortex and Skyrmion crystals. An inhomogeneous mean-field treatment shows that the superfluid (SF) phases inherit these exotic magnetic orders from the MI and display, in addition, unusual modulated current patterns. We present a slave-boson theory which gives insight into such intertwined spin-charge orders in the SF, and discuss signatures of these orders in Bragg scattering, in situ microscopy, and dynamic quench experiments.

Theory of Strain-Controlled Magnetotransport and Stabilization of the Ferromagnetic Insulating Phase in Manganite Thin Films

We show that applying strain on half-doped manganites makes it possible to tune the system to the proximity of a metal-insulator transition and thereby generate a colossal magnetoresistance (CMR) response. This phase competition not only allows control of CMR in ferromagnetic metallic manganites but can be used to generate CMR response in otherwise robust insulators at half-doping. Further, from our realistic microscopic model of strain and magnetotransport calculations within the Kubo formalism, we demonstrate a striking result of strain engineering that, under tensile strain, a ferromagnetic charge-ordered insulator, previously inaccessible to experiments, becomes stable.

Novel magnetic state in

We show that the interplay of strong Hubbard interaction

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Mott insulators

and spin-orbit coupling

Proximity effect and Majorana bound states in clean semiconductor nanowires coupled to disordered superconductors

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Effects of large induced superconducting gap on semiconductor Majorana nanowires

in systems with

Striped Ferronematic ground states in a spin-orbit coupled spin-1 Bose gas

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Spin-orbit Coupling in Optical Lattices

electronic configuration leads to several unusual magnetic phases. Most notably, we find that competition between superexchange and spin-orbit coupling leads to a phase transition from a nonmagnetic state predicted by atomic physics to a novel magnetic state in the large-

Conductance spectroscopy of nontopological-topological superconductor junctions

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