Analysis of Strong-Coupling Parameters for Superfluid 3He

Superfluid $^{3}$He experiments show strong deviation from the weak-coupling limit of the Ginzburg-Landau theory, and this discrepancy grows with increasing pressure. Strong-coupling contributions to the quasiparticle interactions are known to account for this effect and they are manifest in the five $\beta$-coefficients of the fourth order Ginzburg-Landau free energy terms. The Ginzburg-Landau free energy also has a coefficient $g_{z}$ to include magnetic field coupling to the order parameter. From NMR susceptibility experiments, we find the deviation of $g_{z}$ from its weak-coupling value to be negligible at all pressures. New results for the pressure dependence of four different combinations of $\beta$-coefficients, $\beta$_{345}, $\beta$_{12}, $\beta$_{245}, and $\beta$_{5} are calculated and comparison is made with theory.Comment: 6 pages, 2 figures, 1 table. Manuscript prepared for QFS200

Topological superfluid 3^3He-B: fermion zero modes on interfaces and in the vortex core

Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, topology allows us to determine generic features of their fermionic spectrum, which are robust to perturbation and interaction. We discuss the nodeless 3D system, such as superfluid $^3$He-B, vacuum of Dirac fermions, and relativistic singlet and triplet supercondutors which may arise in quark matter. The systems, which have nonzero value of topological invariant, have gapless fermions on the boundary and in the core of quantized vortices. We discuss the index theorem which relates fermion zero modes on vortices with the topological invariants in combined momentum and coordinate space.Comment: paper is prepared for Proceedings of the Workshop on Vortices, Superfluid Dynamics, and Quantum Turbulence held on 11-16 April 2010, Lammi, Finlan

Response, relaxation and transport in unconventional superconductors

We investigate the collision-limited electronic Raman response and the attenuation of ultrasound in spin-singlet d-wave superconductors at low temperatures. The dominating elastic collisions are treated within a t-matrix approximation, which combines the description of weak (Born) and strong (unitary) impurity scattering. In the long wavelength limit a two-fluid description of both response and transport emerges. Collisions are here seen to exclusively dominate the relaxational dynamics of the (Bogoliubov) quasiparticle system and the analysis allows for a clear connection of response and transport phenomena. When applied to quasi-2-d superconductors like the cuprates, it turns out that the transport parameter associated with the Raman scattering intensity for B1g and B2g photon polarization is closely related to the corresponding components of the shear viscosity tensor, which dominates the attenuation of ultrasound. At low temperatures we present analytic solutions of the transport equations, resulting in a non-power-law behavior of the transport parameters on temperature.Comment: 22 pages, 3 figure

Magnetization plateau in the spin ladder with the four-spin exchange

The magnetization process of the $S$=1/2 antiferromagnetic spin ladder with the four-spin cyclic exchange interaction at T=0 is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value if the ratio of the four- and two-spin exchange coupling constants $J_4$ is larger than the critical value $J_{4c}=0.05\pm$0.04. The phase transition with respect to $J_4$ at $J_{4c}$ is revealed to be the Kosterlitz-Thouless-type.Comment: 4 pages, Revtex, with 5 eps figure

Open su(4)-invariant spin ladder with boundary defects

The integrable su(4)-invariant spin-ladder model with boundary defect is studied using the Bethe ansatz method. The exact phase diagram for the ground state is given and the boundary quantum critical behavior is discussed. It consists of a gapped phase in which the rungs of the ladder form singlet states and a gapless Luttinger liquid phase. It is found that in the gapped phase the boundary bound state corresponds to an unscreened local moment, while in the Luttinger liquid phase the local moment is screened at low temperatures in analogy to the Kondo effect.Comment: Revtex 9 pages, published in PR

RECENT EXPERIMENTS IN SUPERFLUID 3He

On présente une revue du travail expérimental récent dans l'3He superfluide concernant la résonance magnétique, les effets d'orientation des distorsions dans les nuages électroniques des atomes d'3He qui comportent les paires de Cooper, et les expériences à haute résolution sur pendule de torsion, y compris les mesures de ρs/ρ et de η. Un effort est fait pour discuter de quelle façon les expériences diverses se rapportent l'une à l'autre et à notre connaissance de l'3He superfluide.A review is presented of recent experimental work in superfluid 3He involving magnetic resonance, the orienting effects of distortions in the electron clouds of the 3He atoms comprising the Cooper pairs, and the high resolution torsional pendulum experiments including measurements of ρs/ρ and η. An effort is made to discuss various experiments as they relate to each other and to our understanding of superfluid 3He