One of our areas is the topic of superconductivity. Superconductivity is a phenomenon exhibited by some metals at very low temperatures approaching absolute zero (-273 C). At these low temperatures, certain materials lose all resistance to the flow of electrical current and become perfect conductors. First discovered in 1911, superconductivity continues to provide major theoretical and experimental challenges to the physics and materials research communities. In the past decade and a half, new classes of superconductors have been discovered at a phenomenal rate.
In a superconductor, electrons pair up in what are called Cooper pairs and the pairs condense into the superconducting state. In conventional superconductors, the pairing of electrons is mediated through the electron-lattice (or electron-phonon) interaction, which is well-understood. In the newer high Tc superconductors and other exotic superconductors, the mechanism remains a matter of debate. Our work has been focussed on examining models for various types of superconductors and calculating experimental observables which can be compared with data. We have worked on conventional superconductors. Indeed, we are one of the most expert groups in the world and hold the largest archive of electron-phonon spectral functions derived from tunneling experiments, along with sophisticated computer codes for solving the nonlinear BCS-Eliashberg equations. Also, we have worked on doped-fullerenes, the high Tc cuprates, two-band superconductors such as MgB2, spin glass superconductors, etc.
Our main research area these days is on the topic of graphene, related Dirac and Weyl materials, and topological insulators. Only as recently as 2004 was graphene (a single sheet of carbon atoms) isolated for the first time. This material has very unusual properties where the electrons act like they have no mass. The simple tight-binding Hamiltonian for this system maps onto a relativistic Dirac equation for fermions in two-dimensions. Graphene is therefore a solid state analogue system for studying this Hamiltonian and providing a venue for experimental tests for predictions for this QED 2+1 theory. On a practical side, this material may be very important for microelectronics. Due to the linear quasiparticle dispersion leading to a linear density of electronic states at the Fermi level, some aspects of graphene are similar to the D-density wave model discussed in the context of the high Tc cuprates and hence it is natural to extend our research efforts to graphene. Graphene is a semimetal or zero-gap semiconductor. When placed in a field effect transistor, it can be doped with electrons or holes, which allows for a detailed examination of the nature of the Dirac electrons. A bilayer of graphene can be configured to produce a tunable semiconductor gap. As an example of our work, we have calculated optical properties of graphene and bilayer graphene. See our publication list for our more recent work.