# Research interests

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, quantum magnetism, fractional quantum Hall effect, low-dimensional superconductivity, and spin-incoherent Luttinger liquids.

## Transition Metal Oxides

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. Along this line, we are actively collaborating with experimentalist Prof. Jak Chakhalian and have helped to provide a theoretical underpinning for exotic phases he has observed. The other direction is the search for topological phases, particularly topological insulators, including strongly interacting varieties beyond the standard Z2 characterization. (For a two-dimensional example see here and for a three-dimensional example see here.)

## Quantum Spin Liquids

We have studied a number of different Gamma-matrix generalizations of the Kitaev model. We have found an exactly solvable chiral spin liquid model that realizes a stable spin Fermi surface with an odd number of electrons per unit cell, the first such example. We have also carried out the first study of an exactly solvable disordered magnetic system with topological properties. In close analogy to the "Topological Anderson Insulators", we find that disorder can stabilize a topological phase. In a recent study, we have shown that a large fraction of the known time-reversal symmetry broken quantum spin liquids (topological and non-topological, gapped and gapless, Fermi surface and Fermi points) can be found in a single exactly solvable model.

## Topological Insulators

Besides establishing some interesting topological connections between quantum spin liquids and topological insulators, we have focused on interaction effects in topological insulators and their possible realization in transition metal oxide heterostructures, as well as a number of different lattice geometries: decorated honeycomb, square-octagon, ruby lattice. We have found a novel "QSH*" phase with topologically protected *collective modes* and a non-trivial ground state degenerarcy, which is also Z2 trivial in the single-particle sense. In addition, we have discovered a "weak topological Mott insulator" phase which will possess topologically protected thermal transport along a certain class of bulk defects. We have also investigated doping effects in the Kane-Mele-Hubbard model. Our work on a flat-band lattice model for fractional quantum Hall effect/fractional topological insulators shows the ruby lattice model is the among the best discovered so far.

## Fractional Quantum Hall Effect

We have focused most of our attention on experimental proposals for investigating mesoscopic effects in non-Abelian quantum Hall systems as part of an effort to provide good experimental tests for non-Abelian statistics. We have established that the charge fluctuations on a quantum dot tunnel coupled to the edge of a non-Abelian quantum Hall state of the Read-Rezayi type exhibit "topologically protected non-Fermi liquid impurity physics" of the channel-isotropic, multi-channel Kondo model-type. We have also considered cases of two dots and multiple dots tunnel coupled to the edge in various geometries. We believe some novel quantum impurity fixed-points may be present in this system.

## Low-dimensional Superconductivity

While superconductivity is an old subject, there are still some interesting questions that appear in heterogenous and nanoscale systems. In collaboration with my experimental colleague Prof. Ken Shih we have investigated the quenching of superconductivity in nanoscale grains as the volume is reduced, and explained how the proximity effect propagates in thin-film heterogeneous superconductors. The latter article was selected as the June 2012 **Nature Physics** Cover Article

## Spin-incoherent Luttinger liquids

Our group has been involved in the study of spin-incoherent Luttinger liquids for some time. Recent work has been done in collaboration with Prof. Adrian Feiguin, an expert in DMRG. We have studied some of the cross-over regions not accessible with analytical methods and also shown that spin-incoherent-like physics can be found in the ground state of some strongly correlated systems.