Ginzburg-Landau Regime Research Articles

On the existence of nematic-superconducting states in the Ginzburg–Landau regime

In this article, we investigate the existence of nematic-superconducting states in the Ginzburg–Landau regime, both analytically and numerically. From the configurations considered, a slab and a cylinder with a circular cross-section, we demonstrate the existence of geometrical thresholds for the obtention of non-zero nematic order parameters. Within the frame of this constraint, the numerical calculations on the slab reveal that the competition or collaboration between nematicity and superconductivity is a complex energy minimization problem, requiring the accommodation of the Ginzburg–Landau parameters of the decoupled individual systems, the sign of the bi-quadratic potential energy relating both order parameters and the magnitude of the applied magnetic field. Specifically, the numerical results show the existence of a parameter regime for which it is possible to find mixed nematic-superconducting states. These regimes depend strongly on both the applied magnetic field and the potential coupling parameter. Since the proposed model corresponds to the weak coupling regime, and since it is a condition on these parameters, we design a test to decide whether this condition is fulfilled.

NMR Frequency Shifts and Phase Identification in Superfluid $$^3\hbox {He}$$

The pressure dependence of the order parameter in superfluid $^3$He is amazingly simple. In the Ginzburg-Landau regime, i.e. close to $T_c$, the square of the order parameter can be accurately measured by its proportionality to NMR frequency shifts and is strictly linear in pressure. This behavior is replicated for superfluid $^3$He imbibed in isotropic and anisotropic silica aerogels. The proportionality factor is constrained by the symmetry of the superfluid state and is an important signature of the corresponding superfluid phase. For the purpose of identifying various new superfluid states in the $p$-wave manifold, the order parameter amplitude of $^3$He-A is a useful reference, and this simple pressure dependence greatly facilitates identification.

Muon spin rotation in heavy-electron pauli-limit superconductors

The formalism for analyzing the magnetic field distribution in the vortex lattice of Pauli limited heavy electron superconductors is applied to the evaluation of the vortex lattice static linewidth relevant to Muon Spin Rotation ($\mu$SR) experiment. On the basis of the Ginzburg-Landau expansion for the superconductor free energy we study the evolution with respect to external field of the static linewidth both in the limit of independent vortices (low magnetic field) and in the near $H_\mathrm{c2}^\mathrm{p}(T)$ regime by using an extension of the Abrikosov analysis to Pauli limited superconductors. We conclude that in the Ginzburg-Landau regime with Pauli limit, the electrodynamics of the vortex lattice predicts anomalous variations with applied field of the static linewidth which is a result of the spin response contribution to screening supercurrents that dominates the usual charge response. The model is proposed as a benchmark for comparison with possible other effects including vortex core localized states or interplay with magnetism.

Depairing current behavior in superconductingNb∕Pd81Ni19bilayers

We have investigated superconductor/ferromagnetic bilayers consisting of $\mathrm{Nb}∕{\mathrm{Pd}}_{81}{\mathrm{Ni}}_{19}$ with varying thickness of the ferromagnet (F) layer ${d}_{F}$ in order to compare the behavior of the superconducting transition temperature ${T}_{c}$ with that of the depairing current density ${J}_{\mathit{dp}}$. For ${T}_{c}({d}_{F})$, we find the usual behavior, with a minimum around ${d}_{F}=3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, which signifies the transition to an oscillatory order parameter in the $F$ layer. For ${J}_{\mathit{dp}}$, which was measured down to $T∕{T}_{c}\ensuremath{\approx}0.5$ using a pulsed-current technique, we find that the behavior can be well described by the Kupriyanov-Lukichev (KL) theory (Fiz. Nizk. Temp. 6, 445 (1980) [Sov. J. Low Temp. Phys. 6, 210 (1980)]), and therefore also by ${J}_{\mathit{dp}}\ensuremath{\propto}{(1\ensuremath{-}T∕{T}_{c})}^{3∕2}$ in the Ginzburg-Landau (GL) regime close to ${T}_{c}$. Extrapolating the GL regime to $T=0$ yields ${J}_{\mathit{dp}}^{\mathit{GL}}(0)$, which, as a function of ${d}_{F}$, behaves similarly to ${T}_{c}({d}_{F})$ with a shallow minimum around ${d}_{F}=3\char21{}4\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. At some temperature below ${T}_{c}$, most samples break away from the KL curve to higher values of ${J}_{\mathit{dp}}$, indicating a current-induced breakdown of the inhomogeneous state. Moreover, we find a significantly increased width of the transition to the normal state in the regime of the oscillatory order parameter.

Quench dynamics of a superfluid Fermi gas

With an eye toward the interpretation of so-called 'cosmological' experiments performed on the low-temperature phases of {sup 3}He, in which regions of the superfluid are destroyed by local heating with neutron radiation, we have studied the behavior of a Fermi gas subjected to uniform variations of an attractive BCS interaction parameter {lambda}. In {sup 3}He, the quenches induced by the rapid cooling of the 'hot spots' back through the transition may lead to the formation of vortex loops via the Kibble-Zurek mechanism. A consideration of the free energy available in the quenched region for the production of such vortices reveals that the Kibble-Zurek scaling law gives at best a lower bound on the defect spacing. Further, for quenches that fall far outside the Ginzburg-Landau regime, the dynamics on the pair subspace, as initiated by quantum fluctuations, tends irreversibly to a self-driven steady state with a gap {delta}{sub {infinity}}={epsilon}{sub C}(e{sup 2/N(0){lambda}}-1){sup -1/2}. In weak coupling, this is only half the BCS gap, the extra energy being taken up by the residual collective motion of the pairs.

Thomas-Fermi approximation to static vortex states in superfluid trapped atomic gases

We revise the Thomas-Fermi approximation for describing vortex states in Bose condensates of magnetically trapped atoms. Our approach is based on considering the hbar -> 0 limit rather than the N -> infinity limit as Thomas-Fermi approximation in close analogy with the Fermi systems. Even for relatively small numbers of trapped particles we find good agreement between Gross-Pitaevskii and Thomas-Fermi calculations for the different contributions to the total energy of the atoms in the condensate. We also discuss the application of our approach to the description of vortex states in superfluid fermionic systems in the Ginzburg-Landau regime.

Comparison of phase boundaries between kagomé and honeycomb superconducting wire networks

We measure resistively the mean-field superconducting-normal phase boundaries of both kagome and honeycomb wire networks immersed in a transverse magnetic field. In addition to their agreement with theory about the overall shapes of phase diagrams, they show striking one-to-one correspondence between the cusps in the honeycomb and kagome phase boundaries. This correspondence is due to their geometric arrangements and agrees with Lin and Nori's recent calculation. We also find that for the frustrated honeycomb network at f=1/2, the current patterns in the superconducting phase differ between the low-temperature London regime and the higher-temperature Ginzburg-Landau regime near T_c.

Vortices in trapped superfluid fermi gases.

We consider a superfluid of trapped fermionic atoms and study the single vortex solution in the Ginzburg-Landau regime. We define simple analytical estimates for the main characteristics of the system, such as the vortex core size, temperature regimes for the existence of a vortex, and the effects of rotation and interactions with normal fermions. The parameter dependence of the vortex core size (healing length) is found to be essentially different from that of the healing length in metallic superconductors or in trapped atomic Bose-Einstein condensation in the Thomas-Fermi limit. This is an indication of the importance of the confining geometry for the properties of fermionic superfluids.

Vortex state of ad-wave superconductor at low temperatures

A systematic perturbation theory is developed to describe the magnetic field-induced subdominant $s$- and $d_{xy}$-wave order parameters in the mixed state of a $d_{x^2-y^2}$-wave superconductor, enabling us to obtain, within weak-coupling BCS theory, analytic results for the free energy of a d-wave superconductor in an applied magnetic field $H_{c1}\ltsim H\ll H_{c2}$ from $T_c$ down to very low temperatures. Known results for a single isolated vortex in the Ginzburg-Landau regime are recovered, and the behavior at low temperatures for the subdominant component is shown to be qualitatively different. In the case of subdominant $d_{xy}$ pair component, superfluid velocity gradients and an orbital Zeeman effect are shown to compete in determining the vortex state, but for realistic field strengths the latter appears to be irrelevant. On this basis, we argue that recent predictions of a low-temperature phase transition in connection with recent thermal conductivity measurements are unlikely to be correct.

Upper Critical Field in Layered Superconductors

The theoretical statements about a restoration of a superconductivity at magnetic fields higher than the quasiclassical upper critical field and a reentrance of superconductivity at temperatures $T_c(H)\approx T_c(0)$ in the superconductors with open Fermi surfaces are reinvestigated taking into account a scattering of quasiparticles on the impurities. The system of integral equations for determination of the upper critical field parallel to the conducting planes in a layered conventional and unconventional superconductors with impurities are derived. The $H_{c2}(T)$ values for the "clean" case in the Ginzburg-Landau regime and at any temperature in the "dirty" case are found analytically. The upper limit of the superconductor purity when the upper critical field definately has a finite value is established.

Microscopic theory of weakly coupled superconducting multilayers in an external magnetic field

We present the first fully microscopic, self-consistent, and self-contained theory of superconducting weakly coupled periodic multilayers with tunnel barriers in the presence of externally applied parallel magnetic fields, in the local Ginzburg-Landau regime. We solve a nontrivial mathematical problem of a microscopic derivation and exact minimization of the free-energy functional. In the thin-layer limit that corresponds to the domain of validity of the phenomenological Lawrence-Doniach model, our physical results strikingly contrast with those of our predecessors. In particular, we completely revise previous calculations of the lower critical field and refute the concept of a triangular Josephson vortex lattice. We show that Josephson vortices penetrate into all the barriers simultaneously and form peculiar structures that we term ''vortex planes''. We calculate the superheating field of the Meissner state and predict hysteresis in the magnetization. In the vortex state, the magnetization exhibits distinctive oscillatory behavior and jumps due to successive penetration of the vortex planes. We prove that the vortex-plane penetration and pinning by the edges of the sample cause the Fraunhofer pattern of the critical Josephson current. We calculate the critical temperature and the upper critical field of infinite (along the layers) multilayers. For finite multilayers, we predict a series of first-order phase transitions to the normal state and oscillations of the critical temperature versus the applied field. Finally, we discuss some theoretical and experimental implications of the obtained results. PACS numbers: 74.50.+r, 74.80.Dm

Unusual Doppler Effect in theBPhase of SuperfluidH3e

We calculate the unusual Doppler effect in the $B$ phase of superfluid ${}^{3}\mathrm{He}$ in the Ginzburg-Landau regime and at low temperatures. We analyze the nontrivial dependence of the sound velocities and of the internal Doppler-shift coefficients on the superfluid velocity in the Ginzburg-Landau regime. The value of the fourth-sound Doppler-shift coefficient is most remarkable: it exceeds 2.2 (the intuitive order of magnitude is 1).

Periodic oscillations of the critical temperature versus the applied magnetic flux in a four-terminal SQUID

Small changes in the critical temperature, which are periodic in the applied magnetic flux, are observed in a four-terminal SQUID, i.e. a SQUID interrupted by a four-terminal Josephson junction. This novel effect is discussed for a conventional two-terminal SQUID, consisting of a weak constriction, by applying thermodynamics in the Ginzburg-Landau regime. Special attention is paid to the case of a SQUID ring with very small self-inductance in an applied magnetic flux of an odd amount of half magnetic flux quanta so that no circulating current is present. An extension is made to the case of the four-terminal SQUID to demonstrate that the theory for the two-terminal SQUID also applies to the experimentally used four-terminal case.

Effect of diffusive boundaries on surface superconductivity in unconventional superconductors.

Boundary conditions for a superconducting order parameter at a diffusive scattering boundary are derived from microscopic theory. The results indicate that for all but isotropic gap functions the diffusive boundary almost completely suppresses surface superconductivity in the Ginzburg-Landau regime. This indicates that in anisotropic superconductors surface superconductivity can only be observed for surface normals along high-symmetry directions where atomically clean surfaces can be cleaved. \textcopyright{} 1996 The American Physical Society.

Supercurrent flow through an effective double-barrier structure.

Supercurrent flow is studied in a structure that in the Ginzburg-Landau regime can be described in terms of an effective double barrier potential. In the limit of strongly reflecting barriers, the passage of Cooper pairs through such a structure may be viewed as a realization of resonant tunneling with a rigid wave function. For interbarrier distances smaller than $d_0=\pi\xi(T)$ no current-carrying solutions exist. For distances between $d_0$ and $2d_0$, four solutions exist. The two symmetric solutions obey a current-phase relation of $\sin(\Delta\varphi/2)$, while the two asymmetric solutions satisfy $\Delta\varphi=\pi$ for all allowed values of the current. As the distance exceeds $nd_0$, a new group of four solutions appears, each contaning $(n-1)$ soliton-type oscillations between the barriers. We prove the inexistence of a continuous crossover between the physical solutions of the nonlinear Ginzburg-Landau equation and those of the corresponding linearized Schr\"odinger equation. We also show that under certain conditions a repulsive delta function barrier may quantitatively describe a SNS structure. We are thus able to predict that the critical current of a SNSNS structure vanishes as $\sqrt{T'_c-T}$, where $T'_c$ is lower than the bulk critical temperature.

Time-dependent Ginzburg-Landau equations for finite-gap superconductors and the problem of paraconductivity

An account for the interference between superfluid and normal motions of charge carriers in the time-dependent Ginzburg-Landau (TDGL) regime turns out to be important and allows one to derive the well-known Maki-Thompson contribution to the paraconductivity using solely the TDGL scheme of description

Superconductivity of quasi-one-dimensional conductors in a high magnetic field.

We determine the phase diagram of a quasi-one-dimensional superconductor (weakly coupled chains system with an open Fermi surface) in a magentic field. A field H(0,H,0) along the y direction (perpendicular the direction x of highest conductivity) tends to confine the electronic motion in the z direction. At low temperature, this effect cannot be neglected and the Ginzburg-Landau theory breaks down. We find that the usual Ginzburg-Landau regime is followed, when the field is increased, by a cascade of superconducting phases separated by first-order transitions, which ends with a strong reentrance of the superconducting phase where the chains interact by Josephson coupling. This high-field superconductivity can survive even in the presence of Pauli pair breaking because the quasi-one-dimensional Fermi surface allows one to construct a Larkin-Ovchinnikov-Fulde-Ferrell state that can exist far above the Pauli-limited field. Moreover, elastic scattering does not destroy the superconducting phases in clean materials with sufficiently large anistropy. We show that the superconducting state evolves from an Abrikosov vortex lattice in weak field towards a Josephson vortex lattice in the reentrant phase. Between these two limits, the order parameter and the current distribution show a laminar-type symmetry. The relevance of our results is discussed for quasi-one-dimensional organic superconductors and quasi-two-dimensional superconductors.

Quasi-one-dimensional superconductors in strong magnetic field.

We determine the phase diagram of a quasi-one-dimensional superconductor (weakly coupled chains system with an [ital open] [ital Fermi] [ital surface]) in a magnetic field. The usual Ginzburg-Landau regime is followed, when the field is increased, by a [ital cascade] of superconducting phases separated by first-order transitions, which ends in a strong reentrance of the superconducting phase. These new phases show a novel kind of symmetry of a laminar type. The Zeeman splitting does not completely suppress the reentrance in very strong field, the ground state being in this case a Larkin-Ovchinnikov-Fulde-Ferrell state.

Localization, superconductivity and magnetic field in a quasi-1D conductor

We show that the quasi-1D aspect of the electronic motion leads to new developments in the physics of localization. In a conductor with an open Fermi surface, the magnetic field makes the electronic motion more and more one-dimensional, in the sense that it confines the wave functions on the chains. Therefore, the effect of disorder is stronger when the field is increased. As a consequence, a strong magnetic field induces a crossover to a 1D localized state. We also extend the original work of A.G. Lebed' on the phase diagram of BCS quasi-1D superconductors in a magnetic field. The usual Ginzburg-Landau regime is followed, when increasing the field, by a series of superconducting phases. The first order transitions between these phases are related to commensurability effects between the periodicity of the order parameter and the distance between chains. The order parameter and the current distribution of these new phases show a new symmetry (of laminar type) which has never been observed or predicted in other systems.

Quasi-one-dimensional superconductors in strong magnetic field

We determine the phase diagram of a quasi-one-dimensional conductor (weakly coupled chains system with an open Fermi surface) in a magnetic field. The usual Ginzburg-Landau regime is followed, when the field is increased, by a cascade of superconducting phases separated by first order transitions, which ends with a strong reentrance of the superconducting phase. These new phases show a novel kind of symmetry of laminar type. The Zeeman splitting does not completely suppress the reentrance in very strong field, the ground state being in this case a Larkin-Ovchinnikov-Fulde-Ferrell state