Unconventional Pairing in Heavy Fermion Metals

The Fermi-liquid theory of superconductivity is applicable to a broad range of systems that are candidates for unconventional pairing. Fundamental differences between unconventional and conventional anisotropic superconductors are illustrated by the unique effects that impurities have on the low-temperature transport properties of unconventional superconductors. For special classes of unconventional superconductors the low-temperature transport coefficients are {\it universal}, i.e. independent of the impurity concentration and scattering phase shift. The existence of a universal limit depends on the symmetry of the order parameter and is achieved at low temperatures $k_B T \ll \gamma \ll \Delta_0$, where $\gamma$ is the bandwidth of the impurity induced Andreev bound states. In the case of UPt$_3$ thermal conductivity measurements favor an $E_{1g}$ or $E_{2u}$ ground state. Measurements at ultra-low temperatures should distinguish different pairing states.Comment: 8 pages in a LaTex (3.0) file plus 5 Figures in PostScript. To appear in the Proceedings of the XXI International Conference on Low Temperature Physics held in Prague, 8-14 August 199

E1gE_{1g} model of superconducting UPt3_3

The phase diagram of superconducting UPt$_3$ is explained in a Ginzburg-Landau theory starting from the hypothesis that the order parameter is a pseudo-spin singlet which transforms according to the $E_{1g}$ representation of the $D_{6h}$ point group. We show how to compute the positions of the phase boundaries both when the applied field is in the basal plane and when it is along the c-axis. The experimental phase diagrams as determined by longitudinal sound velocity data can be fit using a single set of parameters. In particular the crossing of the upper critical field curves for the two field directions and the apparent isotropy of the phase diagram are reproduced. The former is a result of the magnetic properties of UPt$_3$ and their contribution to the free energy in the superconducting state. The latter is a consequence of an approximate particle-hole symmetry. Finally we extend the theory to finite pressure and show that, in contrast to other models, the $E_{1g}$ model explains the observed pressure dependence of the phase boundaries.Comment: RevTex, 29 pages, 18 PostScript figures in a uuencoded, gzipped tar file. PostScript version of paper, tar file of PostScript figures and individual PostScript figures are also available via anonymous ftp at ftp://nym.physics.wisc.edu/anonymou/papers/upt3

Influence of a magnetic field on the antiferromagnetic order in UPt_3

A neutron diffraction experiment was performed to investigate the effect of a magnetic field on the antiferromagnetic order in the heavy fermion superconductor UPt_3. Our results show that a field in the basal plane of up to 3.2 Tesla, higher than H_c2(0), has no effect: it can neither select a domain nor rotate the moment. This has a direct impact on current theories for the superconducting phase diagram based on a coupling to the magnetic order.Comment: 7 pages, RevTeX, 3 postscript figures, submitted to Phys. Rev.

Superconductivity in heavy-fermion U(Pt,Pd)3 and its interplay with magnetism

The effect of Pd doping on the superconducting phase diagram of the unconventional superconductor UPt3 has been measured by (magneto)resistance, specific heat, thermal expansion and magnetostriction. Experiments on single- and polycrystalline U(Pt1-xPdx)3 for x<= 0.006 show that the superconducting transition temperatures of the A phase, Tc+, and of the B phase, Tc-, both decrease, while the splitting DTc increases at a rate of 0.30(2)K/at.%Pd. We find that DTc(x) correlates with an increase of the weak magnetic moment m(x) upon Pd doping. This provides further evidence for Ginzburg-Landau scenarios with magnetism as the symmetry breaking field, i.e. the 2D E representation and the 1D odd parity model. Only for small splittings DTc is proportional to m^2(Tc+) (DTc<= 0.05 K) as predicted. The results at larger splittings call for Ginzburg-Landau expansions beyond 4th order. The tetracritical point in the B-T plane persists till at least x= 0.002 for B perpendicular to c, while it is rapidly suppressed for B||c. Upon alloying the A and B phases gain stability at the expense of the C phase.Comment: 25 pages text (PS), 8 pages with 14 figures (PS), submitted to Phys.Rev.

Contour models of cellular adhesion

The development of traction-force microscopy, in the past two decades, has created the unprecedented opportunity of performing direct mechanical measurements on living cells as they adhere or crawl on uniform or micro-patterned substrates. Simultaneously, this has created the demand for a theoretical framework able to decipher the experimental observations, shed light on the complex biomechanical processes that govern the interaction between the cell and the extracellular matrix and offer testable predictions. Contour models of cellular adhesion, represent one of the simplest and yet most insightful approach in this problem. Rooted in the paradigm of active matter, these models allow to explicitly determine the shape of the cell edge and calculate the traction forces experienced by the substrate, starting from the internal and peripheral contractile stresses as well as the passive restoring forces and bending moments arising within the actin cortex and the plasma membrane. In this chapter I provide a general overview of contour models of cellular adhesion and review the specific cases of cells equipped with isotropic and anisotropic actin cytoskeleton as well as the role of bending elasticity.Comment: 24 pages, 9 figures. arXiv admin note: text overlap with arXiv:1304.107

From 2D to 3D: novel nanostructured scaffolds to investigate signalling in reconstructed neuronal networks

To recreate in vitro 3D neuronal circuits will ultimately increase the relevance of results from cultured to whole-brain networks and will promote enabling technologies for neuro-engineering applications. Here we fabricate novel elastomeric scaffolds able to instruct 3D growth of living primary neurons. Such systems allow investigating the emerging activity, in terms of calcium signals, of small clusters of neurons as a function of the interplay between the 2D or 3D architectures and network dynamics. We report the ability of 3D geometry to improve functional organization and synchronization in small neuronal assemblies. We propose a mathematical modelling of network dynamics that supports such a result. Entrapping carbon nanotubes in the scaffolds remarkably boosted synaptic activity, thus allowing for the first time to exploit nanomaterial/cell interfacing in 3D growth support. Our 3D system represents a simple and reliable construct, able to improve the complexity of current tissue culture models

Thin Polymer Brush Decouples Biomaterial's Micro-/Nano-Topology and Stem Cell Adhesion

Surface morphology and chemistry of polymers used as biomaterials, such as tissue engineering scaffolds, have a strong influence on the adhesion and behavior of human mesenchymal stem cells. Here we studied semicrystalline poly(ε-caprolactone) (PCL) substrate scaffolds, which exhibited a variation of surface morphologies and roughness originating from different spherulitic superstructures. Different substrates were obtained by varying the parameters of the thermal processing, i.e. crystallization conditions. The cells attached to these polymer substrates adopted different morphologies responding to variations in spherulite density and size. In order to decouple substrate topology effects on the cells, sub-100 nm bio-adhesive polymer brush coatings of oligo(ethylene glycol) methacrylates were grafted from PCL and functionalized with fibronectin. On surfaces featuring different surface textures, dense and sub-100 nm thick brush coatings determined the response of cells, irrespective to the underlying topology. Thus, polymer brushes decouple substrate micro-/nano-topology and the adhesion of stem cells