I am interested in several areas of theoretical condensed matter physics.
I currently work on high-temperature superconductivity in the iron-based superconductors. These materials, discovered a year and a half ago, have broken the monopoly of cuprates on high-temperature superconductors. Their pairing symmetry, pairing mechanism, nature of local VS itinerant electrons, and other overwhelming parts of their physics are not known. Along with my collaborators, I have predicted the pairing symmetry in these materials to be a novel-type of s-wave. Along with my post-doc , we have developed a functional renormalization group treatment of the asymmetry of the s-wave gap predicted in the iron-based superconductors.
I also actively work in the field of topological phases and Fractional Quantum Hall effect. These phases exhibit new topological excitations, including exotic non-abelian ones which could potentially be used as qubits of a quantum computer protected from local perturbations. I have worked on a series of FQH states which are described by a remarkable series of polynomials known in mathematics as Jack polynomials. I am also interested in the entanglement spectrum of these systems, and in devising methods to indentify topological order directly from the ground-state wavefunction. I am also interested in any possible classification of topological order in gapless systems.
I also have other interests in the field of topological insulators, in which I predicted the first material to exhibit the Quantum Spin Hall effect. I am interested in how the interactions and disorder modify the nature of edge states. I am also interested in the physics of systems with spin-orbit coupling (insulators, semiconductors and metals), and in new symmetries and effects (such as persistent spin density helixes) existent in these systems.