Graphene, a two-dimensional sheet of graphite, is another good example of a quantum condensed matter system. The pseudo-relativistic dispersion relation with Fermi velocity v_F ~ 10^6 m/sec is intimately connected to the sublattice structure: the basis of the graphene honeycomb lattice contains two carbon atoms, giving rise to an isospin degree of freedom. Graphene has also been suggested as new material system for device applications. Recently we have stuided whether quantum wires with quantized conductance can be formed in graphene. Such electron waveguides are indispensable parts of any conceivable all-graphene device. For narrow graphene ribbons or electrostatically formed graphene wires, conventional conductance quantization seems unlikely. We proposed that by designing a suitable inhomogeneous magnetic field, a magnetic waveguide can be built that indeed allows for the perfectly quantized two-terminal conductance 4e^2/h (including spin and valley degeneracy) even when disorder is present.

Recent Past Interest:
Recently, we have calculated (first) sound velocity in a Fermi superfluid along the BEC-BCS crossover. There is a good agreement of our theoretical prediction on the sound velocity around the unitarity regime with the experimental results at Duke University . We have calculated multibranch Anderson-Bogoliubov modes in the three different regimes: molecular BEC, unitarity and wek-coupling BCS regimes. We have also studied dynamic structure factor and momentum transferred to the superfluid due to the Bragg pulses. The multibranch nature of the spectrum in different regimes along the crossover can be observed in a Bragg scattering experiment. I have presented my results on low-energy properties of Fermi superfluid along the BEC-BCS crossover at various places in India. You can have a look at this presentation, of course, if you wish.

By using the coarse-grain hydrodynamic approach, we are able to obtain an analytic expression for the low energy collective modes of a rotating Fermi superfluid containing large number of vortices along the BEC-BCS crossover. In the fast rotating regime, the molecular BEC enters into the lowest Landau level, similar to the atomic BEC. However, the superfluid in the unitarity and the BCS regimes occupies many low-lying Landau-level like states, in contrast to the usual electronic BCS theory. The difference between the breathing mode frequencies at the BEC and unitarity limit shrinks to zero as the rotation speed approaches the radial trap frequency, in contrast to the finite difference in the non-rotating systems.

I am also interested about correlated bosons in optical lattices. A stack of layers of quasi-two-dimensional Bose condensates can be created by applying strong one-dimensional optical lattice along the symmetry axis of a cigar shaped BEC. We have analyzed the multibranch Bogoliubov-Bloch spectrum (MBBS) in a stack of layers of quasi-two-dimensional Bose condensates. We have shown that couplings of the phonon mode with the radial inhomogeneous density are important to characterize the MBBS properly. We have calculated dynamic structure factor and momentum transferred to the system due to the Bragg pulses. The MBBS can be observed in the Bragg spectroscopy experiments.

Past Interest:
I have also worked on the vortex nucleation and quantum melting of vortex lattices in atomic BECs. I have worked on the Bragg spectroscopy, Hunbary-Brown-Twiss (HBT) effect, the universality of breathing mode, and time-evolution of a certain class of trapped Bose system and also the phase coherence properties in low-dimensional Bose systems.

I have also worked on fractional quantum Hall effect in a heterostructure semiconductor systems. Particularly, we have shown by modeling that two magnetorotons form a bound state in the low-energy limit of one-third quantum Hall state.