Our group is interested in studying the properties of quantum many-body systems with unusual properties, particularly those that result from strong spin-orbit coupling and/or interactions. Much of our current effort is focused on transition metal oxides, topological insulators, topological metals, quantum magnetism, and non-equilibrium phenomena in these materials.
Transition Metal Oxides (Heterostructures)
While the study of transition metal oxides has been active for decades, there are several new angles of study that are particularly ripe for discovery. One is the recent experimental advances in growing high-quality interfaces and heterostructures. One recent joint experimental-theoretical work from our group focused on NdNiO3 grown under different substrate strain conditions. The work, appearing in Nature Communications, showed the thin films possess an interesting phase diagram with a magnetic insulating state, a non-Fermi liquid metallic state, and an insulating state with no detected magentic order down to the lowest temperatures measured--a quantum spin liquid candidate. Another direction is the search for topological phases, particularly topological insulators. We have focused on thin films grown along the  crystalline direction, and have written an invited review covering our work and that of others in this area. Bilayers of LaNiO3 have received signficant attention in our group, and we have also made an effort to make our predictions as reaslistic as possible, including first-principles predictions of structural distortions. We have also focused on bilayers and trilayers of Y2Ir2O7 grown along  and used both density functional theory (DFT) and dynamical mean field theory (DMFT) to study correlation effects. The main candidate topological state in these systems is the Chern insulator, or quantum anomalous Hall state (QAH).
Interacting Topological Insulators
One of the areas that remains at the forefront of the field of topological insulators is the effect of correlations on driving fundamentally new topological states. In this regard, the fractional quantum Hall effect is the archetype. However, the discovery of time-reversal invariant topological insulators has shown us the fractional quantum Hall effect is only the tip of the iceberg of theoretical possibilities. Our group has predicted a number of possible new phases that possess time-reversal symmetry, but are not adiabatically connected to the non-interacting electron system: in two-dimensions, the "quantum spin Hall star" (QSH*) phase, and in three-dimensions the "weak topological Mott insulator" (WTMI), the "topological crystalline Mott insulator" (TCMI), and the "topological insulator star" (TI*) phase. We have co-authored a review in Nature Physics on this topic. Away from fractionalized topological states, we have used Quantum Monte Carlo (QMC) to study the simultaneous interplay of disorder, interactions, and topology in a fermion sign-free model, and found that the symmetry of the Hamiltonian can have a powerful influence on the competition of these factors.
The study of topological insulators has given rise to a number of new directions in condensed matter physics: One of these is the subject of topological metals. Dirac metals and Weyl semi-metals are important examples of topological metals. They each possess linearly dispersing electronic band structure (in all three spatial dimensions) near the Fermi energy. A number of unusual properties have been predicted for this class of materials, including an unusual magnetoelectric response and Fermi arcs in the surface Brillouin zone, observable by angle resolved photoemission spectroscopy (ARPES). Our group's effort in this area has focused on unusual termoelectric transport in Weyl/Dirac systems and in double-Weyl systems. The Weyl/Dirac systems show a characteristic magnetic field dependence when the field is aligned along the thermal gradient, and the double-Weyl systems exhibit certain spatial anistropies that allow them to be distinguished from the single Weyl systems. In addition, we have also investigated how topological metals may have a highly tunable electronic cooling.
Our group has worked on various aspects of quantum magnetism for many years, including the study of models of quantum spin liquids--states describing a collection of local moments that do not order even at zero temperature! Most recently we have focused on local moment models inspired by transition metal oxides with strong spin-orbit coupling, such as the iridates. For models relevant to (Li,Na)2IrO3, we have found an exceptionally rich phase diagram with a number of unusual orders. Our work on thin film Y2Ir2O7 has revealed topological magnonon bands and unconventional superconducity, upon doping. We have also focused effort on one-dimensional spin chains and investigated how the momentum-space entananglement spectrum reflects (or not) universal properties of these systems.
One of the most exciting frontiers in condensed matter physics is the study of quantum many-particle systems out-of-equilibrium. A natural experimental scenario is the "pump-probe" situation where a "pump" laser takes a material out-of-equilibrium and a "probe" laser is used to measure the properties of the excited system after some time delay with respect to the "pump". In the limit of a long pump pulse width, the systems experiences an approximately time-periodic Hamiltonian and a Floquet description is relevant. It remains an experimental challenge to observe topological transitions in electronic band structure. Our work has focused on more realistic multi-band systems than have been considered previously.