Triangular Pair Density Wave in Confined Superfluid

Recent advances in experiment and theory suggest that superfluid ^{3}He under planar confinement may form a pair density wave (PDW) whereby superfluid and crystalline orders coexist. While a natural candidate for this phase is a unidirectional stripe phase predicted by Vorontsov and Sauls in 2007, recent nuclear magnetic resonance measurements of the superfluid order parameter rather suggest a two-dimensional PDW with noncollinear wave vectors, of possibly square or hexagonal symmetry. In this Letter, we present a general mechanism by which a PDW with the symmetry of a triangular lattice can be stabilized, based on a superfluid generalization of Landau's theory of the liquid-solid transition. A soft-mode instability at a finite wave vector within the translationally invariant planar-distorted B phase triggers a transition from uniform superfluid to PDW that is first order due to a cubic term generally present in the PDW free-energy functional. This cubic term also lifts the degeneracy of possible PDW states in favor of those for which wave vectors add to zero in triangles, which in two dimensions uniquely selects the triangular lattice.

Quasicondensation in Two-Dimensional Fermi Gases.

In this paper we follow the analysis and protocols of recent experiments, combined with simple theory, to arrive at a physical understanding of quasi-condensation in two dimensional Fermi gases. A key signature of quasi-condensation, which contains aspects of Berezinskii-Kosterlitz-Thouless behavior, is a strong zero momentum peak in the pair momentum distribution. Importantly, this peak emerges at a reasonably well defined onset temperature. The resulting phase diagram, pair momentum distribution, and algebraic power law decay are compatible with recent experiments throughout the continuum from BEC to BCS.

Axisymmetric scattering of scalar waves by spheroids.

A phase shift formulation of scattering by oblate and prolate spheroids is presented, in parallel with the partial-wave theory of scattering by spherical obstacles. The crucial step is application of a finite Legendre transform to the Helmholtz equation in spheroidal coordinates. In the long-wavelength limit the spheroidal analog of the spherical scattering length immediately gives the cross section. Analytical results are readily obtained for scattering of Schrödinger particle waves by impenetrable spheroids, and for scattering of sound waves by acoustically soft spheroidal objects. The method is restricted to scattering by spheroids whose symmetry axis is coincident with the direction of the incident plane wave.

Constraints on spheroidal beam wavefunctions.

The oblate spheroidal wavefunctions proposed by Rodríguez-Morales and Chávez-Cerda are shown to be possible representations of physical beams only when the angular function S(mn)(ß,η) has odd n-m. This condition makes S(mn) odd in η, which ensures the convergence of integrals of physical quantities over a cross section of the beam. The odd n-m condition also makes S(mn)(ß,η) zero in the focal plane z=0 outside the circle ρ=b, and thus allows for the physically necessary discontinuity in phase at z=0 on the ellipsoidal surfaces of otherwise constant phase. Only a subset of the oblate spheroidal functions can be exact representations of nonparaxial scalar beams.

Investigation of particle shape and size effects in SERS using T-matrix calculations.

The influence of particle size and shape effects on average and punctual surface-enhanced Raman scattering (SERS) enhancement factors (EFs) is investigated using exact T-matrix electrodynamic calculations of silver and gold spheroids over a large parameter space. This study extends the conventional treatment of these effects within the frameworks of the electrostatics approximation, its generalizations, or Mie theory for spheres. It confirms the qualitative features of these approaches, but provides in addition quantitative predictions of SERS EFs in the case of large non-spherical particles, where the lightning-rod effect (shape effect) and radiation damping (size effect) operate simultaneously. Finally, the localization effect at large SERS EF (hot-spots) is shown to be dictated only by shape, not size, in the case of metallic spheroids at the dipolar localized surface plasmon resonance.