Skyrmions in arbitrarily polarized quantum Hall states

We derive an effective non-linear 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 have obtained recently 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 get attached to the electrons in order to form composite fermions.Comment: 6 page

Inhomogeneous longitudinal electric field-induced anomalous Hall conductivity in a ferromagnetic two-dimensional electron gas

It is known that the anomalous Hall conductivity (AHC) in a disordered two dimensional electron system with Rashba spin-orbit interaction and finite ferromagnetic spin-exchange energy is zero in the metallic weak-scattering regime because of the exact cancellation of the bare-bubble contribution by the vertex correction. We study the effect of inhomogeneous longitudinal electric field on the AHC in such a system. We predict that AHC increases from zero (at zero wavenumber), forms a peak, and then decreases as the wavenumber for the variation of electric field increases. The peak-value of AHC is as high as the bare-buble contribution. We find that the wave number, q, at which the peaks occur is the inverse of the geometric mean of the mean free path of an electron and the spin-exchange length scale. Although the Rashba energy is responsible for the peak-value of AHC, the peak position is independent of it.Comment: 5 pages, 4 figure

Ginzburg-Landau theory of noncentrosymmetric superconductors

The data of temperature dependent superfluid density $n_s(T)$ in Li$_2$Pd$_3$B and Li$_2$Pt$_3$B [Yuan {\it et al.}, \phrl97, 017006 (2006)] show that a sudden change of the slope of $n_s (T)$ occur at slightly lower than the critical temperature. Motivated by this observation, we microscopically derive the Ginzburg-Landau (GL) equations for noncentrosymmetric superconductors with Rashba type spin orbit interaction. Cooper pairing is assumed to occur between electrons only in the same spin split band and pair scattering is allowed to occur between two spin split bands. The GL theory of such a system predicts two transition temperatures, the higher of which is the conventional critical temperature $T_c$ while the lower one $T^*$ corresponds to the cross-over from a mixed singlet-triplet phase at lower temperatures to only spin-singlet or spin-triplet (depending on the sign of the interband scattering potential) phase at higher temperatures. As a consequence, $n_s (T)$ shows a kink at this cross-over temperature. We attribute the temperature at which sudden change of slope occurs in the observed $n_s (T)$ to the temperature $T^*$. This may also be associated with the observed kink in the penetration depth data of CePt$_3$Si. We have also estimated critical field near critical temperature.Comment: 7 pages, 1 figur