Bernoulli potential in type-I and weak type-II supercoductors: II. Surface dipole

The Budd-Vannimenus theorem is modified to apply to superconductors in the Meissner state. The obtained identity links the surface value of the electrostatic potential to the density of free energy at the surface which allows one to evaluate the electrostatic potential observed via the capacitive pickup without the explicit solution of the charge profile.Comment: 7 pages, 1 figur

On the relation between virial coefficients and the close-packing of hard disks and hard spheres

The question of whether the known virial coefficients are enough to determine the packing fraction $\eta_\infty$ at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Pad\'e approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes use of the same virial coefficients and of the equation of state in a form where the packing fraction is explicitly given as a function of the pressure. The results of this approach both for hard-disk and hard-sphere fluids, which can straightforwardly accommodate higher virial coefficients when available, lends support to the conjecture that $\eta_\infty$ is equal to the maximum packing fraction corresponding to an ordered crystalline structure.Comment: 10 pages, 6 figures; v2: discussion about hard-square and hard-hexagon systems on a lattice added; five new reference

Auxiliary field approach to dilute Bose gases with tunable interactions

We rewrite the Lagrangian for a dilute Bose gas in terms of auxiliary fields related to the normal and anomalous condensate densities. We derive the loop expansion of the effective action in the composite-field propagators. The lowest-order auxiliary field (LOAF) theory is a conserving mean-field approximation consistent with the Goldstone theorem without some of the difficulties plaguing approximations such as the Hartree and Popov approximations. LOAF predicts a second-order phase transition. We give a set of Feynman rules for improving results to any order in the loop expansion in terms of composite-field propagators. We compare results of the LOAF approximation with those derived using the Popov approximation. LOAF allows us to explore the critical regime for all values of the coupling constant and we determine various parameters in the unitarity limit.Comment: 16 pages, 7 figure

Multi-threshold second-order phase transition

We present a theory of the multi-threshold second-order phase transition, and experimentally demonstrate the multi-threshold second-order phase transition phenomenon. With carefully selected parameters, in an external cavity diode laser system, we observe second-order phase transition with multiple (three or four) thresholds in the measured power-current-temperature three dimensional phase diagram. Such controlled death and revival of second-order phase transition sheds new insight into the nature of ubiquitous second-order phase transition. Our theory and experiment show that the single threshold second-order phase transition is only a special case of the more general multi-threshold second-order phase transition, which is an even richer phenomenon.Comment: 5 pages, 3 figure

Scanning tunneling spectroscopy of high-temperature superconductors

Tunneling spectroscopy played a central role in the experimental verification of the microscopic theory of superconductivity in the classical superconductors. Initial attempts to apply the same approach to high-temperature superconductors were hampered by various problems related to the complexity of these materials. The use of scanning tunneling microscopy/spectroscopy (STM/STS) on these compounds allowed to overcome the main difficulties. This success motivated a rapidly growing scientific community to apply this technique to high-temperature superconductors. This paper reviews the experimental highlights obtained over the last decade. We first recall the crucial efforts to gain control over the technique and to obtain reproducible results. We then discuss how the STM/STS technique has contributed to the study of some of the most unusual and remarkable properties of high-temperature superconductors: the unusual large gap values and the absence of scaling with the critical temperature; the pseudogap and its relation to superconductivity; the unprecedented small size of the vortex cores and its influence on vortex matter; the unexpected electronic properties of the vortex cores; the combination of atomic resolution and spectroscopy leading to the observation of periodic local density of states modulations in the superconducting and pseudogap states, and in the vortex cores.Comment: To appear in RMP; 65 pages, 62 figure

Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality

We consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS partition function in a generic flat background for the whole L(p,q) family and provide a solution for its large N dynamics; on the other, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and briefly discuss how it could be restored in a non-perturbative setting.Comment: 17 pages, 6 figures; references adde

The Flux-Line Lattice in Superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.Comment: Review paper for Rep.Prog.Phys., 124 narrow pages. The 30 figures do not exist as postscript file