On the Ginzburg–Landau Functional in the Surface Superconductivity Regime

We present new estimates on the two-dimensional Ginzburg–Landau energy of a type-II superconductor in an applied magnetic field varying between the second and third critical fields. In this regime, superconductivity is restricted to a thin layer along the boundary of the sample. We provide new energy lower bounds, proving that the Ginzburg–Landau energy is determined to leading order by the minimization of a simplified 1D functional in the direction perpendicular to the boundary. Estimates relating the density of the Ginzburg–Landau order parameter to that of the 1D problem follow. In the particular case of a disc sample, a refinement of our method leads to a pointwise estimate on the Ginzburg–Landau order parameter, thereby proving a strong form of uniformity of the surface superconductivity layer, which is related to a conjecture by Xing-Bin Pan.     

Universal and shape dependent features of surface superconductivity

We analyze the response of a type II superconducting wire to an external magnetic field parallel to it in the framework of Ginzburg–Landau theory. We focus on the surface superconductivity regime of applied field between the second and third critical values, where the superconducting state survives only close to the sample’s boundary. Our first finding is that, in first approximation, the shape of the boundary plays no role in determining the density of superconducting electrons. A second order term is however isolated, directly proportional to the mean curvature of the boundary. This demonstrates that points of higher boundary curvature (counted inwards) attract superconducting electrons.     

On the reversibility of the Meissner effect and the angular momentum puzzle

It is generally believed that the laws of thermodynamics govern superconductivity as an equilibrium state of matter, and hence that the normal-superconductor transition in a magnetic field is reversible under ideal conditions. Because eddy currents are generated during the transition as the magnetic flux changes, the transition has to proceed infinitely slowly to generate no entropy. Experiments showed that to a high degree of accuracy no entropy was generated in these transitions. However, in this paper we point out that for the length of times over which these experiments extended, a much higher degree of irreversibility due to decay of eddy currents should have been detected than was actually observed. We also point out that within the conventional theory of superconductivity no explanation exists for why no Joule heat is generated in the superconductor to normal transition when the supercurrent stops. In addition we point out that within the conventional theory of superconductivity no mechanism exists for the transfer of momentum between the supercurrent and the body as a whole, which is necessary to ensure that the transition in the presence of a magnetic field respects momentum conservation. We propose a solution to all these questions based on the alternative theory of hole superconductivity. The theory proposes that in the normal-superconductor transition there is a flow and backflow of charge in direction perpendicular to the phase boundary when the phase boundary moves. We show that this flow and backflow explains the absence of Joule heat generated by Faraday eddy currents, the absence of Joule heat generated in the process of the supercurrent stopping, and the reversible transfer of momentum between the supercurrent and the body, provided the current carriers in the normal state are holes.     

Comments upon the superconducting like behaviour observed in lead telluride

Recent a.c. measurements of magnetic susceptibility in PbTe have been interpreted as evidence of anomalous superconductivity of lead precipitates up to temperatures of 20 K. We present here new measurements on this material which can be explained by the properties of eddy currents in the sample without invoking any superconductivity at all.     

On the Third Critical Field in Ginzburg-Landau Theory

Using recent results by the authors on the spectral asymptotics of the Neumann Laplacian with magnetic field, we give precise estimates on the critical field, , describing the appearance of superconductivity in superconductors of type II. Furthermore, we prove that the local and global definitions of this field coincide. Near only a small part, near the boundary points where the curvature is maximal, of the sample carries superconductivity. We give precise estimates on the size of this zone and decay estimates in both the normal (to the boundary) and parallel variables.The two authors are supported by the European Research Network ‘Postdoctoral Training Program in Mathematical Analysis of Large Quantum Systems’ with contract number HPRN-CT-2002-00277, and the ESF Scientific Programme in Spectral Theory and Partial Differential Equations (SPECT). Part of this work was carried out while S.F. visited CIMAT, Mexico.     

Surface Superconductivity¶in Applied Magnetic Fields Above HC2

In this paper we study the surface superconductivity phenomenon of type 2 superconductors under applied magnetic fields above the critical field . We show that, for a cylindrical superconductor of infinite height placed in a homogeneous applied magnetic field, H e ₃, with H lying in between and keeping away from and , superconductivity persists uniformly at a thin sheath surrounding the entire lateral surface of the sample. As the applied field decreases gradually, superconductivity in the surface sheath becomes strong and develops into a surface superconducting state, while the interior of the sample remains close to the normal state. Received: 21 May 2001 / Accepted: 11 February 2002     

Superconductivity on the border of weak itinerant ferromagnetism in UCoGe

We report the coexistence of ferromagnetic order and superconductivity in UCoGe at ambient pressure. Magnetization measurements show that UCoGe is a weak ferromagnet with a Curie temperature T(C)=3 K and a small ordered moment m(0)=0.03 micro(B). Superconductivity is observed with a resistive transition temperature T(s)=0.8 K for the best sample. Thermal-expansion and specific-heat measurements provide solid evidence for bulk magnetism and superconductivity. The proximity to a ferromagnetic instability, the defect sensitivity of T(s), and the absence of Pauli limiting, suggest triplet superconductivity mediated by critical ferromagnetic fluctuations.     

Synchronization of slow-fast systems

We provide an overview over the following eleven contributions on superconductivity in copper-oxygen and iron-based compounds. The main objective of this volume is an improved general understanding of superconductivity at high transition temperatures. The key questions on the way towards understanding superconducting pairing beyond electron-phonon coupling are spelled out, and the present status of theoretical reasoning is summarized. The crucial experiments, their results and interrelations are discussed. The central result is that fluctuations of spin and charge contribute substantially to superconductivity and also to other ordering phenomena. Methodically, the simultaneous analysis of results obtained from different experimental techniques such as photoelectron spectroscopy and neutron scattering, on one and the same sample, turned out to be of pivotal importance.     

Competing boundary interactions in a Josephson junction network with an impurity

We analyze a perturbation of the boundary Sine-Gordon model where two boundary terms of different periodicities and scaling dimensions are coupled to a Kondo-like spin degree of freedom. We show that, by pertinently engineering the coupling with the spin degree of freedom, a competition between the two boundary interactions may be induced, and that this gives rise to nonperturbative phenomena, such as the emergence of novel quantum phases: indeed, we demonstrate that the strongly coupled fixed point may become unstable as a result of the “deconfinement” of a new set of phase-slip operators — the short instantons — associated with the less relevant boundary operator. We point out that a Josephson junction network with a pertinent impurity located at its center provides a physical realization of this boundary double Sine-Gordon model. For this Josephson junction network, we prove that the competition between the two boundary interactions stabilizes a robust finite coupling fixed point and, at a pertinent scale, allows for the onset of 4e superconductivity.     

Magnetoresistivity and filamentary superconductivity in nickel-doped BaFe_2As_2

We present magnetotransport studies on a series of BaFe_(2-x)Ni_xAs_2(0.03 ≤ x ≤ 0.10) single crystals. In the underdoped(x = 0.03) non-superconducting sample, the temperature-dependent resistivity exhibits a peak at 22 K, which is associated with the onset of filamentary superconductivity(FLSC). FLSC is suppressed by an external magnetic field in a manner similar to the suppression of bulk superconductivity in an optimally-doped(x = 0.10) compound, suggesting the same possible origin as the bulk superconductivity. Our magnetoresistivity measurements reveal that FLSC persists up to the optimal doping and disappears in the overdoped regime where the long-range antiferromagnetic order is completely suppressed, pointing to a close relation between FLSC and the magnetic order.     

Microstructural analysis of Nd1.85Ce0.15CuO4−y superconductor sintered under high pressure and ambient pressure

The microstructure of Nd_1.85Ce_0.15CuO_4−y superconductor sintered under high pressure and ambient pressure has been characterized by scanning electron microscopy (SEM) and high-resolution transmission electron microscopy (HREM). It has been observed that the conventional sample is porous, while the high-pressure sample is almost pore-free. It is confirmed that the thermal treatment under high pressure recovers fairly well connections between grains which were partly crushed during the compression process; hence the weak links at grain boundary are improved. Furthermore, a high density of defects induced by pressure is observed in the high-pressure sample. In contrast, the conventional sample is nearly perfect. For comparison, the microstructure of a sample pressed at high pressure at room temperature is also examined. The influence of pressure on the microstructure and the superconductivity is discussed.     

Bulk superconducting phase with a full energy gap in the doped topological insulator Cu(x)Bi₂Se₃

The superconductivity recently found in the doped topological insulator Cu(x)Bi?Se? offers a great opportunity to search for a topological superconductor. We have successfully prepared a single-crystal sample with a large shielding fraction and measured the specific-heat anomaly associated with the superconductivity. The temperature dependence of the specific heat suggests a fully gapped, strong-coupling superconducting state, but the BCS theory is not in full agreement with the data, which hints at a possible unconventional pairing in Cu(x)Bi?Se?. Also, the evaluated effective mass of 2.6m(e) (m(e) is the free electron mass) points to a large mass enhancement in this material.     

Relaxation processes in mesoscopic superconductors

We investigate the possibility of a novel kind of optical pump probe spectroscopy where the two laser pulses are focused on different areas of the sample. The response to the destruction of the superconducting state in a large part of a mesoscopic ring is studied numerically. We use the time dependent Ginzburg-Landau equations with periodic boundary conditions and external magnetic field. We evaluate the relaxation rates of the superconducting order parameter as well as the voltage induced by the charge imbalance. Computer simulations confirm that the perturbation of superconductivity on one part of the ring induces a voltage which decelerates the superconducting electrons on the other part of the ring. This deceleration results in the decrease of the superconducting current and the superfluid density. The relaxation times are of the order of the picosecond, the induced voltage of few millivolts and the variation of the superconducting gap of 10% which we believe to be suitable for time resolved femtosecond optical spectroscopy.     

Strongly correlated superconductivity in Rh17S15

In this Letter, we report resistivity, susceptibility, heat capacity, and upper critical field studies on a polycrystalline Rh17S15 sample which exhibits superconductivity below 5.4 K. Detailed studies suggest that the superconductivity in this compound arises from strongly correlated charge carriers presumably due to the high density of states of Rh d bands at the Fermi level. Moreover, the Hall coefficient shows a sign change and increases at low temperature before the sample becomes a superconductor below 5.4 K.     

Two-dimensional organic superconductors studied by NMR under pressure

The (BEDT)₂X family of layered superconductors is one of the largest among nearly 50 organic superconductors currently known. One of the advantages of the organic compounds as prototype materials for studying the mechanisms of superconductivity is their relatively high sensitivity to hydrostatic pressure. We review recent NMR studies of these compounds using NMR under liquid and gas pressure. We focus on the low temperature part of the phase diagram where the physics is controlled by electronic correlations leading to a competition between magnetism and superconductivity. This interplay between different ground states is shown by the observation of a pseudo-gap and antiferromagnetic fluctuations and can be finely tuned by the application of pressure. Using a gas pressure system gives the unique possibility of sweeping the pressure at low temperature. Recently we used this technique to study the AF-SC boundary and established the existence of a first order transition line between the superconducting and antiferromagnetic states. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fate of the peak effect in a type-II superconductor: multicriticality in the Bragg-Glass transition

We have used small-angle neutron scattering (SANS) and ac magnetic susceptibility to investigate the global magnetic field H vs temperature T phase diagram of a Nb single crystal in which a first-order transition of Bragg-glass melting (disordering), a peak effect, and surface superconductivity are all observable. It was found that the disappearance of the peak effect is directly related to a multicritical behavior in the Bragg-glass transition. Four characteristic phase boundary lines have been identified on the H-T plane: a first-order line at high fields, a mean-field-like continuous transition line at low fields, and two continuous transition lines associated with the onset of surface and bulk superconductivity. All four lines are found to meet at a multicritical point.     

Domain-wall guided nucleation of superconductivity in hybrid ferromagnet-superconductor-ferromagnet layered structures

Domain-wall superconductivity is studied in a superconducting Nb film placed between two ferromagnetic Co/Pd multilayers with perpendicular magnetization. The parameters of top and bottom ferromagnetic films are chosen to provide different coercive fields, so that the magnetic domain structure of the ferromagnets can be selectively controlled. From the dependence of the critical temperature Tc on the applied magnetic field H, we have found evidence for domain-wall superconductivity in this three-layered F/S/F structure for different magnetic domain patterns. The phase boundary, calculated numerically for this structure from the linearized Ginzburg-Landau equation, is in good agreement with the experimental data.     

Vortex entry and nucleation of antivortices in a mesoscopic superconducting triangle

The nucleation of superconductivity in mesoscopic equilateral triangles is investigated by using the linearized Ginzburg-Landau equation (LGLE). The trigonal symmetry of the sample has a profound effect on the superconducting state in the presence of a magnetic field H leading, in particular, to the formation of antivortices in symmetry-consistent states. For the same given irreducible representation, vortices enter always by three via the middle of the edges, approach the center, and then are dispatched towards the corners of the triangle. The measured superconducting phase boundary T(c)(H) is in good agreement with the T(c)(H) line found from the LGLE.     

Direct evidence for negative grain boundary potential in Ca-doped and undoped YBa2Cu3O7-x

Using electron holography in a transmission electron microscope, we obtained direct evidence for the reduction of negative charge at grain boundary dislocations in Ca-doped YBa2Cu3O7 (YBCO) when compared to undoped YBCO. Because of the finite width of the valence band in the superconducting CuO2 planes, the negative grain boundary charge can lead to a depletion of electron holes available for superconductivity. A significant reduction in the size of the perturbed region in the Ca-doped samples appears to be the principal mechanism for the improved interfacial superconductivity.     

Formation of superconductivity through interparticle interactions in ferrimagnetic-like Sn nanoparticle assemblies

We report on the observation of the development of superconductivity through interparticle interactions in 3, 5, 7, and 23 nm ferrimagnetic-like Sn nanoparticle assemblies. The Sn nanoparticles are fabricated using the gas condensation method. Each sample consists of a macroscopic amount of individual Sn nanoparticles without a capping molecule. Ferrimagnetism is found but no sign of superconductivity can be detected when the 3 nm particles are very loosely assembled. A reduction in the mean particle moment results when the packing fraction of the assembly is increased. Superconductivity occurs when a critical packing fraction is reached. Beyond this, the superconducting transition temperature T _C continues to increase and noticeably exceeds that of the bulk T _C. The enhancement of superconductivity by interparticle interactions has also been observed in 5, 7, and 23 nm particle assemblies, with the effect becoming less significant in larger particles. We attribute these observations to the transfer of electrons between the surface and the core regions of the nanoparticles triggered by finite size effects and interparticle interactions.