Current problems in condensed matter physics are intriguing and challenging. This field appeals to me the most because its current trends encompass a whole range of diverse topics and have important implications. Specifically, I am interested in topological phases and approaches to achieve fault tolerant quantum computation, strongly correlated electron systems as well as many-body physics of ultracold atoms and quantum gases.
Manipulation of a system of multiple spins being used as qubits for information processing is problematic due to decoherence. I am interested in exploring proposals for quantum information processing that are robust against decoherence such as topological quantum computation, diamond quantum computer etc. In the first case, theoretical investigation of detection and manipulation of anyons obeying non-abelian statistics is important and I am interested to explore whether and how we could use Majorana fermions as candidate for robust information processing. I am curious about theory and design of experiments through which we can learn how to perform operations on topologically encoded data. Recent proposal of a T-junction of conventional and topological superconductor to exchange Majorana fermions to encode information is an exciting idea. I also look forward to the prospect of using diamond Nitrogen Vacancy (NV) centers as robust qubits since these qubits can be manipulated even at room temperature due to the environment free from magnetic noise. Spins of Nitrogen electrons at carbon vacancies can be manipulated via an external field to create immune qubits which might form the basis for a quantum turing machine. That research in this direction is at its prime, is well supported by the recent developments of a way to create self-assembling scalable diamond qubit system with help from biological intelligence and the proven ability to link NV centers 3 meters apart.
I am interested in theoretical description of Quantum spin Hall states and study of novel properties due to modified Maxwell"s laws inside topological insulator. Besides the proposed exotic particles settling open questions in particle physics, the field is exciting because we might see a path for topological quantum computation using Majorana fermions in hybrid topological insulators. I am also interested in the study of strongly correlated electron systems. It is remarkable that dynamical mean field theory (DMFT) which is used to model these electrons whose competition between localization and itinerancy shows up in the Hamiltonian, has been a success in modeling phase diagrams of many materials. I am interested in applications of DMFT to a broader class of materials including inhomogeneous materials such as disordered alloys or interfaces.