Note, however, that in the cold fermion systems with a Feshbach resonance, the superfluidity is interaction-generated (rather than proximity induced as in the proposals for condensed matter systems). With the important techniques already developed, the realization of topological physics in cold atomic systems now seems tantalizingly close to experimental reach. These include spin-orbit coupling in 1D systems, photoemission spectroscopy, etc. We will continue to develop concrete schemes for realizing TS states and the associated topological phase transitions using experimental techniques which have already been realized. In these systems, I wrote the very first paper on using an artificially generated spin-orbit coupling, Zeeman field, and s-wave superfluid interactions to create topological superfluid states and MFs (this paper, Physical Review Letters 101, 160401 (2008), in fact, had the genesis of the idea that was later applied to the condensed matter systems to propose Majorana fermions in semiconductor-superconductor heterostructures).

These states will also be investigated with regard to their Fermi surface topology, the quantum oscillation signatures of the Fermi surfaces, and the diamagnetic response/Nernst effect, as well as their transport signatures in the pseudogap phase.Ĭold atom systems in optical traps and lattices: Past experimental breakthrough at NIST realizing spin-orbit coupling for ultra-cold atoms opened exciting new possibilities for the observation of novel topological superfluid phases in cold atomic systems. We will focus on the magnetic excitation spectrum of these states that follows from their collective mode spectrum and compare it with the neutron scattering experiments. These include the electronic nematic state, charge density wave state, and the loop current state within the CuO unit cell without broken translational symmetry. Additionally, we will also consider other candidate phases for the pseudogap regime which are close in energy with the DDW state. I plan on exploring aspects of the DDW state such as the collective mode spectrum and the neutron scattering signatures in the pseudogap regime of the cuprates. These include pronounced Nernst and other thermoelectric effects, diamagnetism, aspects of the neutron scattering, and the polar Kerr effect (an indication of broken time-reversal symmetry) above T_c in the underdoped regime of the cuprates. I have been able to explain many exciting experimental results in the framework of the DDW theory of the pseudogap phase. D work we helped develop the theory and phenomenology of the d-density wave state (DDW, a version of the staggered flux state) applicable to the underdoped regime of the cuprates. This body of work has given rise to a new sub-field - TS states in spin-orbit coupled semiconductor heterostructures - and has recently seen a great flurry of activities.Ĭuprate high-temperature superconductivity: In my Ph. In past works, I proposed schemes for realizing TS states and MFs in semiconductor heterostructures spurring leading experimental groups worldwide to experimentally look for MF excitations in the proposed systems. In this sense, this research is intimately connected to research in quantum computation. The Majorana condition is at the heart of non-Abelian quantum statistics and, as proposed by Kitaev, can potentially serve as building blocks for a topological quantum computer. The TS states I focus on support a certain kind of unusual zero energy quantum states in various order parameter defects which satisfy the Majorana condition. Majorana more than seven decades ago, have recently made a decisive and convincing comeback to condensed matter physics in part due to the efforts of my work and those of my collaborators in the last few years. MFs, which were introduced in high energy physics by the Italian physicist E.

Majorana fermions and topological quantum computation: We are interested in topological superconducting (TS) states to realize Majorana fermion (MF) quasiparticles in the order parameter defects of systems with strong spin-orbit (SO) interactions for use in quantum computation. Condensed matter theory, Majorana fermions and topological quantum computation, physics of high-temperature superconductors, cold atom systems in optical traps and lattices:

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