V. Ravishankar

EFFECTIVE P, T RESTORATION IN CHERN–SIMONS SUPERCONDUCTIVITY

We present an analysis of the finite temperature Chern–Simons superconductivity model within the mean field framework. Using analytical and numerical means we compute the changes in the magnetic susceptibility, conductivity, the dielectric constant, and the specific heat as the temperature is increased. Over a narrow range of temperatures the properties of the system show a smooth transition to the normal state. Accompanying this is the near vanishing of the off-diagonal conductivity, signifying the effective restoration of parity and time reversal symmetries.

SKYRMIONS IN ARBITRARILY POLARIZED QUANTUM HALL STATES

We derive an effective nonlinear sigma model for quantum Hall systems with arbitrary polarizations, by employing the recently proposed doublet model. We study the topological excitations, in particular the Skyrmions, as a function of the filling fraction as well as the polarization. We determine the relationship between the topological charge density and the electronic charge density, and the statistics of Skyrmions. We also estimate the value of spin stiffness by using the dispersion relations that we recently obtained by employing the time-dependent Hartree-Fock approximation for the doublet model. Finally, we point out how the Skyrmionic excitations reveal information directly on the number of flux tubes that become attached to the electrons in order to form composite fermions.

Direct test of the composite-fermion model in quantum Hall systems

We show that neutron scattering and Raman scattering experiments can unambiguously determine a composite fermion parameter, viz., the effective number of Landau Levels filled by the composite fermions. For this purpose, one needs partially polarized or more preferably unpolarized quantum Hall states. We further find that spin correlation function acts as an order parameter in the spin transition.

Chern-Simons superconductivity at finite magnetic field

We study Chern-Simons (CS) superconductivity in the presence of uniform external magnetic field of {ital arbitrary} {ital strength} for a system of fermions in two spatial dimensions, which are minimally coupled both to the CS and Maxwell gauge fields. We have carried out the computation within the mean-field ansatz. Analyzing only the mean field (i.e., ignoring the fluctuations of the gauge fields), we find that chemical potential, susceptibility, and magnetization show discontinuities for integer number of filled Landau levels. Taking into account the fluctuations of the gauge fields, we find that the masses of the excitations increase with the magnetic field, and that the presence of nonlinear magnetic susceptibilities shows the absence of any critical or pseudocritical magnetic field. Finally, an interesting result is that, unlike ordinary superconductors, the system is magnetically asymmetric.