arXiv subjects
Publications and source records attributed to V. Ravishankar.
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.
We determine the wave functions for arbitrarily polarized quantum Hall states by employing the doublet model which has been proposed recently to describe arbitrarily polarized quantum Hall states. Our findings recover the well known fully polarized Laughlin wave functions and unpolarized Halperin wave function for the filling fraction $ν=2/5$. We have also confirmed by an explicit One-loop computation that the Hall conductivity does indeed get quantized at those filling fractions that follow from the model. Finally, we have given a physical picture for the non-analytic nature of the wave functions, and shown that quantum fluctuations restore the Kohn mode.
We propose a global model which accounts for all the observed quantum Hall states in terms of an abelian doublet of Chern-Simons gauge fields, with the strength of the Chern-Simons term given by a coupling matrix. The model is employed within the composite fermion picture.
We study quantum Hall systems (mainly the integer case) at finite temperatures and show that there is a novel temperature dependence even for a pure system, thanks to the `anomalous' nature of generators of translation. The deviation of Hall conductivity from its zero temperature value is controlled by a parameter $T_0 =πρ/m^\ast N$ which is sample specific and hence the universality of quantization is lost at finite temperatures.
We study the finite temperature (FT) effects on integer quantum Hall effect (IQHE) and fractional quantum Hall effect (FQHE) as predicted by the composite fermion model. We find that at $T\neq 0$, universality is lost, as is quantization because of a new scale $T_0=πρ/m^\ast p$. We find that this loss is not inconsistent with the experimentally observed accuracies. While the model seems to work very well for IQHE, it agrees with the bulk results of FQHE but is shown to require refinement in its account of microscopic properties such as the effective mass. Our analysis also gives a qualitative account of the threshold temperatures at which the FQHE states are seen experimentally. Finally, we extract model independent features of quantum Hall effect at FT, common to all Chern-Simons theories that employ mean field ansatz.
We study Chern-Simons (CS) superconductivity in the presence of uniform external magnetic field of {\it arbitrary 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. Analysing 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 show the absence of any critical or pseudo critical magnetic field. Finally, an interesting result is that, unlike ordinary superconductors, the system is magnetically asymmetric.