It was recently discovered that the interface between LaAlO3 and SrTiO3  features a variety of fascinating phenomena, such as superconductivity coexisting with ferromagnetism . This is particularly surprising since by themselves, these materials are both electronically trivial insulators. In my study of these systems, together with Prof. Patrick A. Lee and Andrew C. Potter, we introduced a model for the interface electrons which captures their main physical properties . Most significantly, it explained the origin of ferromagnetism and its coexistence with superconductivity. This is made possible by an unconventional Fulde-Ferrel-Larkin-Ovchinikov (FFLO) pairing between electrons supported by spin-orbit coupling.
An additional example of unconventional superconductivity that I have been studying is the odd-parity pairing state. In collaboration with Prof. L. Fu we demonstrated that in materials characterized by chiral symmetry, disorder is not an obstacle to realizing such a superconducting state .
The quantum kinetic approach proved very useful for the analysis of the transverse thermoelectric response, known as the Nernst effect, in disordered superconducting films . We showed that a giant Nernst signal is generated by fluctuations of the superconducting order parameter above the critical temperature or critical magnetic field. Not only does my theory show remarkable agreement with experiments conducted on conventional superconducting films ; it has also been used by the group of Prof. L. Taillefer to explain their Nernst measurements on high temperature superconductors .
Recently, I have completed the theory of transverse transport in the vicinity of the superconducting phase transition, by analyzing the Hall effect. This work combines theoretical  and experimental  studies in close collaboration with Prof. A. M. Finkel'stein and the group of Prof. A. Kapitulnik. We demonstrated that the Hall conductivity, similar to the Nernst effect, is a much more sensitive probe of superconducting fluctuations than regular, longitudinal transport.
A particularly striking example of extremely atypical quasiparticles is found in quantum spin liquids. These can form in the vicinity of the Mott metal-insulator transition when the charge is gapped while the spin degrees of freedom strongly fluctuate. The effective theory for this Mott insulator consists of spinons, which are neutral fermions with spin 1/2. The spinons exhibit a magnetic interactions that, unlike the Coulomb repulsion, is not screened and leads to non-Fermi liquid behavior. I showed that even in the absence of disorder this strong interaction provides an efficient relaxation mechanism for spin and heat currents, keeping them finite even at the lowest temperatures .