Type-IV superconductivity: Cooper pairs with broken inversion and time-reversal symmetries in conventional superconductors

The vortex phase in a singlet superconductor in the absence of impurities is shown to be absolutely unstable with respect to the appearance of a triplet component that breaks both the inversion and time-reversal symmetries of Cooper pairs. The symmetry breaking paramagnetic effects are demonstrated to be of the order of unity if the orbital upper critical field, H_c2(0), is of the order of the Clogston paramagnetic limiting field, H_p. We suggest a generic phase diagram of such a type-IV superconductor that is a singlet one at H = 0 and characterized by a mixed singlet-triplet order parameter with broken time-reversal symmetry in the vortex phase. The possibility to observe type-IV superconductivity in clean organic, high-T_c, MgB₂, and other superconductors is discussed.     

Muon spin rotation in heavy-electron pauli-limit superconductors

The formalism for analyzing the magnetic field distribution in the vortex lattice of Pauli-limit heavy-electron superconductors is applied to the evaluation of the vortex lattice static linewidth relevant to the muon spin rotation (??SR) experiment. Based on the Ginzburg-Landau expansion for the superconductor free energy, we study the evolution with respect to the external field of the static linewidth both in the limit of independent vortices (low magnetic field) with a variational expression for the order parameter and in the near H _c2 ^P (T) regime with an extension of the Abrikosov analysis to Pauli-limit superconductors. We conclude that in the Ginzburg-Landau regime in the Pauli-limit, anomalous variations of the static linewidth with the applied field are predicted as a result of the superconductor spin response around a vortex core that dominates the usual charge-response screening supercurrents. We propose the effect as a benchmark for studying new puzzling vortex lattice properties recently observed in CeCoIn₅.     

Experimental observation of Bose condensation in high-temperature superconductors

Emission Mössbauer spectroscopy on ⁶⁷Cu (⁶⁷Zn) and ⁶⁷Ga (⁶⁷Zn) isotopes was used to show that for the superconductors Nd_1.85Ce_0.15CuO₄, La_1.85 Sr_0.15CuO₄, and Tl₂Ba₂ CaCuO₈ in the temperature range T > T _c the temperature dependence of the center of gravity S of the Mössbauer spectrum is determined by the second-order Doppler shift, while in the range T < T _c the Bose condensation of Cooper pairs influences the value of S (here T _c is the superconducting transition temperature). The spatial nonuniformity produced in the electron density by a Bose condensate of Cooper pairs was observed for La_1.85 Sr_0.15CuO₄.     

Families of solutions to the generalized Ginzburg-Landau equation and structural transitions between them

Solutions to the generalized Ginzburg-Landau equations for superconductors are obtained for a Ginzburg-Landau parameter κ close to unity. The families of solutions with arbitrary number n of flux quanta in a unit cell are analyzed. It is shown that under certain conditions, a cascade of phase transitions between different structures in a magnetic field appears near T _c . Algebraic equations are derived for determining the boundaries of coexistence of different phases on the {T, H ₀} plane.     

Magnetization of type-ii superconductors in the range of fields H c 1 ≤ H ≤ H c 2Variational Method

A variational method is proposed to find the magnetic field dependence of the magnetization of type-II superconductors in the mixed state by a self-consistent technique. This model allows for suppression of the order parameter to zero at the centers of Abrikosov vortices and also for the magnetic field dependence of the order parameter. The results can be applied to the entire range of fields H _c 1 ≤ H ≤ H _c 2 for any values of the Ginzburg-Landau parameter $\kappa > 1/\sqrt 2$ . It is shown that in weak fields where κ ? 1 the behavior of the magnetization can be described exactly in the London approximation provided that the correct value of H _c 1 is used. Near the second critical field this dependence shows good agreement with the well-known Abrikosov result. It is also shown that using the concept of isolated vortices and applying the principle of superposition of the fields and currents generated by these vortices to calculate the magnetization gives inaccurate quantitative results even in fairly weak fields. By going beyond these concepts, it was possible to allow more accurately for the influence of the vortex cores on the magnetization behavior in the intermediate range of fields H _c 1 ?H ? H _c 2 and to identify the range of validity of various approximations used widely in the literature.     

Structure of the superconducting state of superconductors near the critical field Hc2 for values of the Ginzburg-Landau parameter kclose to unity

It is shown that near the transition temperature T _c the coefficients of the second and third terms in the expansion of the free energy in powers of H _c2−B (B is the magnetic field induction inside the superconductor) go to zero simultaneously for a value of κ=1 for the Ginzburg-Landau parameter. Thereby the structure of the mixed state near H _c2 for a value of the parameter κ close to unity is determined by the temperature correction to the coefficient for the third power and the coefficient for the fourth power in the expansion of the free energy in powers of H _c2−B. The values of these coefficients depend on the type of vortex lattice. Zh. éksp. Teor. Fiz. 112, 1499–1509 (October 1997)     

GINZBURG-LANDAU THEORY AND VORTEX LATTICE OF HIGH-TEMPERATURE SUPERCONDUCTORS

The thermodynamics of the vortex lattice of high-temperature superconductors has been studied by solving the generalized Ginzburg-Landau equations derived microscopically. Our numerical simulation indicates that the structure of the vortex lattice is oblique at the temperature far away from the transition temperature T_c, where the mixed s-d_x²-y² state is expected to have the lowest energy. Whereas, very close to T_c, the d_x²-y² wave is slightly lower energetically, and a triangular vortex lattice recovers. The coexistence and the coupling between the s and d waves would account for the unusual dynamic behaviours such as the upward curvature of the upper critical field curve H_C2(T), as observed in dc magnetization measurements on single-crystal YBa₂Cu₃O₇ samples.     

Breakdown of the superheated Meissner state and spontaneous vortex nucleation in type II superconductors

The theory of local stability of the superheated Meissner state presented in an earlier paper is supplemented by an investigation of global stability in two dimensions. We conclude that flux penetration cannot be delayed beyond the fieldH _s1 where local instability sets in. Various new two-dimensional Ginzburg-Landau solutions, obtained numerically, are discussed. These include the lowest saddle point separating the Meissner from the normal and vortex state and a solution resembling the “nascent vortex state” whose existence was postulated recently by Walton and Rosenblum. Using these solutions the process of spontaneous vortex nucleation is discussed.     

Crossover from BCS-superconductivity to Bose-condensation

Starting from a model of free Fermions in two dimensions with an arbitrary strong effective interaction, we derive a Ginzburg-Landau theory describing the crossover from BCS-superconductivity to Bose-condensation. We find a smooth crossover from the standard BCS-limit to a Gross-Pitaevski type equation for the order parameter in a Bose superfluid. The mean field transition temperature exhibits a maximum at a coupling strength, where the behaviour crosses over from BCS to Bose like with corresponding values of 2 Δ₀/T_c ≈ 5 which are characteristic for high T_c superconductors.     

Normal phase and superconducting instability in the attractive Hubbard model: a DMFT(NRG) study

We study the normal (nonsuperconducting) phase of the attractive Hubbard model within the dynamical mean field theory (DMFT) using the numerical renormalization group (NRG) as an impurity solver. A wide range of attractive potentials U is considered, from the weak-coupling limit, where superconducting instability is well described by the BCS approximation, to the strong-coupling region, where the superconducting transition is described by Bose condensation of compact Cooper pairs, which are formed at temperatures much exceeding the superconducting transition temperature. We calculate the density of states, the spectral density, and the optical conductivity in the normal phase for this wide range of U, including the disorder effects. We also present the results on superconducting instability of the normal state dependence on the attraction strength U and the degree of disorder. The disorder influence on the critical temperature T _c is rather weak, suggesting in fact the validity of Anderson’s theorem, with the account of the general widening of the conduction band due to disorder.     

Electron density variation at copper sites at the superconducting transition in cuprates

The temperature dependence of the center of gravity S of the Mössbauer spectrum produced by ⁶⁷Zn²⁺ impurity ions occupying copper and yttrium sites in YBa₂Cu₃O_6.6, YBa₂Cu₃O_6.9, YBa₂Cu₄O₈, Bi₂Sr₂CaCu₂O₈, HgBa₂CuO₄, and HgBa₂CaCu₂O₆ at temperatures above the superconducting transition point T_c was shown to be dominated by the second-order Doppler shift. For T<T_c, the quantity S is affected by the band mechanism associated with the formation of Cooper pairs and their Bose condensation. The variation of electron density at a metal site of the crystal was found to be related to the superconducting transition temperature. The variation of electron density created by the Cooper pair Bose condensate in compounds with two structurally inequivalent copper positions was shown to be different for these copper sites. The experimental dependence of the fraction of superconducting electrons on temperature agrees with the analogous dependence following from BCS theory for all the sites studied.     

Mechanism of high Tc superconductivity and and anti-ferromagnetic order of high Tc oxides

We propose, here, new theory of high T_c superconductivity mechanism. The hole-Cooper pair formation and the Bose condensation of the Cooper pairs occur in the high T_c superconducting oxides such as Bi–Sr–Ca–Cu–O. The atractive interaction is due to the antiferromagnetic order and its fluctuation of CuO₂ plane. Dependence of T_c on the numbers of CuO₂ layers is quantitatively analized.     

Unconventional temperature dependence of the cuprate excitation spectrum

Key properties of the cuprates, such as the pseudogap observed above the criticaltemperature T_c, remain highlydebated. Given their importance, we recently proposed a novel mechanism based on theBose-like condensation of mutually interacting Cooper pairs [W. Sacks, A. Mauger, Y. Noat,Supercond. Sci. Technol. 28, 105014 (2015)]. In this work, we calculate thetemperature dependent DOS using this model for different doping levels from underdoped tooverdoped. In all situations, due to the presence of excited pairs, a pseudogap is foundabove T_c while the normal DOSis recovered at T^?, the pair formation temperature. Asimilar behavior is found as a function of magnetic field, crossing a vortex, where apseudogap exists in the vortex core. We show that the precise DOS shape depends oncombined pair (boson) and quasiparticle (fermion) excitations, allowing for a deeperunderstanding of the SC to the PG transition.     

On the emergence of superconductivity and hysteresis in a cylindrical type I superconductor

One-dimensional vortex-free solutions of the system of Ginzburg-Landau equations (the so-called precursor states) are studied. These states describe the emergence of superconductivity in a long cylindrical type I superconductor, which was initially in the supercooled normal state in a magnetic field, and are formed upon subsequent reduction of the external field. The precursor states are responsible for the magnetic hysteresis in type I superconductors (for which κ < κ_c, where κ_c (R) is the critical value of the parameter κ in the Ginzburg-Landau theory, which is a function of radius). The range of fields is determined in which precursor states exist along with the Meissner state (and a hysteresis is possible) in the dependence of the cylinder radius R and parameter κ.     

Temperature Dependence of the Upper Critical Field in Disordered Hubbard Model with Attraction

We study disorder effects upon the temperature behavior of the upper critical magnetic field in an attractive Hubbard model within the generalized DMFT+Σ approach. We consider the wide range of attraction potentials U—from the weak coupling limit, where superconductivity is described by BCS model, up to the strong coupling limit, where superconducting transition is related to Bose–Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures significantly higher than superconducting transition temperature, as well as the wide range of disorder—from weak to strong, when the system is in the vicinity of Anderson transition. The growth of coupling strength leads to the rapid growth of H_c2(T), especially at low temperatures. In BEC limit and in the region of BCS–BEC crossover H_c2(T), dependence becomes practically linear. Disordering also leads to the general growth of H_c2(T). In BCS limit of weak coupling increasing disorder lead both to the growth of the slope of the upper critical field in the vicinity of the transition point and to the increase of H_c2(T) in the low temperature region. In the limit of strong disorder in the vicinity of the Anderson transition localization corrections lead to the additional growth of H_c2(T) at low temperatures, so that the H_c2(T) dependence becomes concave. In BCS–BEC crossover region and in BEC limit disorder only slightly influences the slope of the upper critical field close to T _c . However, in the low temperature region H_c2 (T may significantly grow with disorder in the vicinity of the Anderson transition, where localization corrections notably increase H_c2 (T = 0) also making H_c2(T) dependence concave.     

Re-entry in ferromagnetic superconductors

The re-entry phenomenon in magnetic superconductors is studied using the generalized Ginzburg-Landau free energy introduced by Blount and Varma. The re-entry temperature T_c2 is simply that temperature at which the magnetization acts as a source of induction strong enough to destroy superconductivity. Above T_c2 ferromagnetism and superconductivity coexist. The structure is an Abrikosov vortex lattice, with ferromagnetic magnetization spreading widely around the vortex cores. Within our approximations, the phase transition at T_c2 is of second order.     

Andreev reflection between a normal metal and the FFLO superconductor II: A self-consistent approach

We consider Andreev reflection in a two dimensional junction between a normal metal and a heavy fermion superconductor in the Fulde–Ferrell (FF) type of the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state. We assume s-wave symmetry of the superconducting gap. The parameters of the superconductor: the gap magnitude, the chemical potential, and the Cooper pair center-of-mass-momentum Q, are all determined self-consistently within a mean-field (BCS) scheme. The Cooper pair momentum Q is chosen as perpendicular to the junction interface. We calculate the junction conductance for a series of barrier strengths. In the case of incoming electron with spin σ = ↑ only for magnetic fields close to the upper critical field H_c2, we obtain the so-called Andreev window, i.e. the energy interval in which the reflection probability is maximal, which in turn is indicated by a peak in the conductance. The last result differs with other non-self-consistent calculations existing in the literature.     

Finite width effect on the upper critical field Hc2 of superconducting networks

A recent prediction for the continuum limit of the upper critical field of infinite superconducting networks H_c2(T)= dH^(bulk)_c2 (d=spatial dimension of the network) is checked experimentally. A direct comparison of the measured critical fields on both samples: film and infinite 2D regular networks, made of the same material, support strongly this theoretical prediction. The deviation of the proportionality coefficient from d=2 is attributed to the finite width of wires. Wires of finite width are shown to be responsible for a renormalization of the diffusion coefficient of Cooper pairs. The expression so obtained for H_c2 as a function of the filling factor is consistent with the measured value.