We study effective actions for order parameter fluctuations at low temperature in layered d-wave superconductors such as the cuprates. The order parameter lives on the bonds of a square lattice and has two amplitude and two phase modes associated with it. The low frequency spectral weights for amplitude and relative phase fluctuations is determined and found to be subdominant to quasiparticle contributions. The Goldstone phase mode and its coupling to density fluctuations in charged systems is treated in a gauge-invariant manner. The Gaussian phase action is used to study both the c-axis Josephson plasmon and the more conventional in-plane plasmon in the cuprates. We go beyond the Gaussian theory by deriving a coarse-grained quantum XY model, which incorporates important cutoff effects overlooked in previous studies. A variational analysis of this effective model shows that in the cuprates, quantum effects of phase fluctuations are important in reducing the zero temperature superfluid stiffness, but thermal effects are small for T ≪ Tc.

Almost all quantum Hall effect to date can be understood as integral quantum Hall effect of appropriate particles, namely electrons or composite fermions. This paper investigates theoretically the feasibility of nested states of composite fermions which would lead to a quantum Hall effect that cannot be understood as integral quantum Hall effect of composite fermions. The weak residual interaction between composite fermions will play a crucial role in the establishment of such quantum Hall states by opening a gap in a partially filled composite-fermion level. To treat the problem of interacting composite fermions, we develop a powerful method that allows us to obtain the low energy spectra at composite fermion fillings of ν * = n +ν without making any assumption regarding the structure of composite fermions in the topmost partially filled level. The method is exact aside from neglecting the composite-fermion Landau level mixing, and enables us to study rather large systems, for example, 24 particles at a total flux of 62 hc/e, for which the dimension of the lowest Landau level Hilbert space is ∼ 10 17 . We have investigated, for fully spin polarized composite fermions, several filling factors between 1/3 and 2/5 using this approach. The results indicate that any possible incompressibility at these fractions is likely to have a fundamentally different origin than that considered earlier.

We report directional point contact Andreev reflection (PCAR) measurements on high-quality single crystals of the noncentrosymmetric superconductor BiPd. The PCAR spectra measured on different crystallographic faces of the single crystal clearly show the presence of multiple superconducting energy gaps. For point contacts with low resistance, in addition to the superconducting gap feature, a pronounced zero-bias conductance peak is observed. These observations provide strong evidence for the presence of an unconventional order parameter in this material.

In our Letter, we estimated that the transition from the conventional partially spin polarized 4=11 fractional quantum Hall state to the unconventional fully spin polarized 4=11 state occurs at κ ≈ 0.025, where κ is the Zeeman splitting measured in units of e 2 =ϵl, with l being the magnetic length and ϵ the dielectric constant of the host semiconductor. This led us to conclude that the 4=11 state observed by Pan et al.[1] at B ¼ 11.25 T, which corresponds to κ ¼ 0.019, is partially spin polarized. However, upon tilting, this experiment observed no transition up to κ ¼ 0.028, indicating that, for the parameters of this experiment, the critical value of κ lies outside the region 0.019-0.028. This implies that the corrections due to finite thickness, Landau level mixing, and disorder are larger than we had expected, and will need to be evaluated more accurately to predict the critical value of κ for a given experimental system.The above issue does not affect the principal result of our Letter, namely the unconventional nature of the fully spin polarized fractional quantum Hall effect at 4=11 and 5=13. Our estimation of the critical value of κ also remains applicable in the limit of zero width, no Landau level mixing, and no disorder.