Superconductivity of heavy fermions in a two-band model

Thermodynamic and electrodynamic properties of heavy-fermion superconductors are studied in a two-band model with interband (“hybrid”) singlet pairing. The general form of electron-electron interaction is analyzed and it is shown in particular that antiferromagnetic spin fluctuations increase the tendency to such a pairing. The expression for the free energy functional is obtained and the behaviour of the correlation length H_c2 and the London penetration depth at T = 0 and T→T_c is investigated. The model discussed gives reasonable qualitative agreement with the properties of heavy-fermion superconductors.     

Superfluid response in heavy fermion superconductors

Motivated by a recent London penetration depth measurement [H. Kim, et al., Phys. Rev. Lett. 114, 027003 (2015)] and novel composite pairing scenario [O. Erten, R. Flint, and P. Coleman, Phys. Rev. Lett. 114, 027002 (2015)] of the Yb-doped heavy fermion superconductor CeCoIn₅, we revisit the issue of superfluid response in the microscopic heavy fermion lattice model. However, from the literature, an explicit expression for the superfluid response function in heavy fermion superconductors is rare. In this paper, we investigate the superfluid density response function in the celebrated Kondo–Heisenberg model. To be specific, we derive the corresponding formalism from an effective fermionic large-N mean-field pairing Hamiltonian whose pairing interaction is assumed to originate from the effective local antiferromagnetic exchange interaction. Interestingly, we find that the physically correct, temperature-dependent superfluid density formula can only be obtained if the external electromagnetic field is directly coupled to the heavy fermion quasi-particle rather than the bare conduction electron or local moment. Such a unique feature emphasizes the key role of the Kondo-screening-renormalized heavy quasi-particle for low-temperature/energy thermodynamics and transport behaviors. As an important application, the theoretical result is compared to an experimental measurement in heavy fermion superconductors CeCoIn5 and Yb-doped Ce_1?xYb_xCoIn₅ with fairly good agreement and the transition of the pairing symmetry in the latter material is explained as a simple doping effect. In addition, the requisite formalism for the commonly encountered nonmagnetic impurity and non-local electrodynamic effect are developed. Inspired by the success in explaining classic 115-series heavy fermion superconductors, we expect the present theory will be applied to understand other heavy fermion superconductors such as CeCu₂Si₂ and more generic multi-band superconductors.     

Static properties of type-II superconductors at arbitrary temperature and induction

A concise expression for the free energy of clean type-II superconductors is given from which magnetization curves, gap and field are easily calculated for 0 < T < T_c and 0 < B < H_c2.     

The vortex-like excitations detected by Nernst signals in high-T c superconductors

The nature of the pseudogap state and its relation to the d-wave superconductivity in high-T _c superconductors is still an open issue. The vortex-like excitations detected by the Nernst effect measurements exist in a certain temperature range above superconducting transition temperature T _c, which strongly support that the pseudogap phase is characterized by finite pairing amplitude with strong phase fluctuations and imply that the phase transition at T _c is driven by the loss of long-range phase coherence. We first briefly introduce the electronic phase diagram and pseudogap state of high-T _c superconductors, and then review the results of Nernst effect for different high-T _c superconductors. Related theoretical models are also discussed.     

Quasi-particle transport in vortex state of nodal superconductors

The quasi-classical approach has proved very useful for studying the vortex state of nodal superconductors like d-wave superconductors in high T_c cuprates. After a brief introduction, we review our work on the thermal conductivity tensor in d-wave superconductors and f-wave superconductors.     

Die Sprungtemperatur von Supraleitern

An iteration procedure allows to find an equation for the critical temperatureT _c of superconductors starting from the linearized Eliashberg equations without using any cutoff parameters or a Coulomb pseudopotential. Explicit calculation ofT _c for a simple model leads to Morel, Anderson and McMillan's^1,2 expression thereby allowing for a physical interpretation of the commonly used approximation for the Coulombpseudopotential.     

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.     

The instability point H s of the Meissner state for large-κ superconductors

The critical field H _s corresponding to the emergence of vortices in a superconductor without a threshold is found near the transition temperature and in the limit as T→0 for an arbitrary value of the depairing factor Γ. In superconductors of the second kind, this field value coincides with the absolute instability point of the Meissner state. In large-κ superconductors, the order parameter tends to zero on the surface of the super-conductor if the external magnetic field reaches the value H _s. We obtain that H _s=H _cm (where H _cm is the thermodynamic critical field) for an arbitrary value of the depairing factor Γin the temperature region near T _c and at T=0.     

A new numerical method for quasi-particle spectroscopy around a pair of vortices in triplet superconductors

Triplet superconductors such as Sr₂RuO₄ and Na_xCoO₂·yH₂O are now found to be p-wave (p_x±ip_y) or f-wave ((p_x±ip_y)coscp_z) superconductors. In conventional singlet superconductors, vortices are quantized because phase of order parameter must rotate by 2π around a vortex. But triplet superconductors have a degree of freedom of spin, which is described by d-vector. The d-vector and phase can rotate by π around a vortex, separately. Therefore appearance of HQVs is predicted. Theoretically, it is found that a pair of HQVs is more stable than a singly quantized vortex, for several parameter regions.In this study, in order to investigate quasi-particle bound states around two vortices in s-wave superconductors, we have developed a new numerical method to solve the BdG equation for two vortices state, using Mathieu functions. We confirmed the validity of this method for two vortices state and applied it in case of a pair of vortices. And we solved it.     

Magnetic hysteresis in type II superconductors

The theories governing the magnetic behavior of Type II superconductors assume reversible magnetization curves. However, due to imperfections and inhomogeneities, many superconductors possess hysteretic curves. A theory is proposed which allows a ‘reversible’ curve to be found from the two irreversible curves. The ‘reversible’ curve is an approximation to the exact Abrikosov reversible curve for H_c1 ≤ H ≤ H_c2. The theory agrees closely with experimental results.     

Current-voltage characteristics of type-II superconductors

For a wide range of samples and conditions the I-V characteristic of type-II superconductors fits the expression V ∞ (I-I_p)² (I-αI_p)⁻¹. The initial non-linearity is attributed to the fact that the fluxons do not move with uniform velocity.     

Energy gaps and transition temperatures of the strong-coupling superconductors,lead and mercury,as functions of the mean free paths of the electrons

The energy gaps and the transition temperatures of the strong-coupling superconductors lead and mercury are measured as functions of the mean free paths of the electrons. The energy gap of lead increases with decreasing mean free path; the transition temperature is found to be constant. The energy gap of mercury runs through a maximum value with decreasing mean free path whereas the transition temperature decreases. The energy gap of pure mercury is extrapolated to the value 1.58 meV and yields the ratio 2Δ₀/kT _c =4.4. The experimental results confirm the theoretical prediction that the attractive electron-electron interaction in disordered superconductors is increased. But in addition, the strong-coupling effect appears to become more important in disordered superconductors. A comparison with similar experiments for weak-coupling superconductors is made.     

Broadening of the specific heat jump in three-dimensional superconductors

The Ginzburg-Landau theory is used to calculate perturbatively the influence of stochastic inhomogeneities on the smearing of the specific heat jump in three-dimensional superconductors. The small-scale and large-scale (compared to the correlation length) inhomogeneities are simultaneously taken into account to derive a finite and continuous (in the vicinity of T _c ) expression for the temperature dependence of the superconductor specific heat.     

Review of superconductivity in BiS2-based layered materials

In 2012, a new layered superconductor where BiS₂ layer is the superconducting layer was discovered. So far, seven types of BiS₂-based superconductors and two related superconductors have been discovered. In this article, the diversity of the crystal structure and the physical properties of the BiS₂-based superconductors are reviewed. Furthermore, notable characteristics of superconductivity in the BiS₂ family are introduced. The prospects for raising T_c in this family are proposed on the basis of experimental and theoretical studies.     

Physical processes in high-temperature superconductors at the interface between the vortex-filled and meissner regions

A technique has been proposed for investigating the magnetic microstate of high-temperature superconductors with a simultaneous analysis of the crystalline microstate of the sample with the aim of elucidating the specific features of the interaction between the crystalline and magnetic microstructures of polycrystalline high-temperature superconductors. Qualitatively new results have been obtained for samples with different microstructures. In particular, it has been found that the magnetic field dependences of the trapped magnetic flux density B _tr(H ₀) of polycrystalline and epitaxial films of high-temperature superconductors exhibit regular steps for both increasing and decreasing magnetic fields. The obtained results have demonstrated that, in strong magnetic fields, the studied epitaxial films, as well as bulk and thin-film polycrystalline high-temperature superconductors, “break down” into single domains, crystallites, and subcrystallites with different demagnetization factors. It has been revealed that the dependences B _tr(H ₀) also exhibit steps due to the simultaneous penetration of vortices into crystallites of approximately the same sizes and into more regularly arranged subcrystallites. As the quality of the samples increases, these steps become more pronounced because of the increase in the short-range order. The absence of steps in the dependence B _tr(H ₀) of the polycrystalline bulk samples clearly demonstrates the absence of long-range order in these samples. It is the vitreousness of the crystallographic microstructure of high-temperature superconductors which is responsible for the observed transformations in the vortex system. The similarity of the results obtained for samples with different microstructures indicates that the penetration (escape), distribution, and trapping of the magnetic flux in these samples occur through a universal mechanism. It has been found that the polycrystalline high-temperature superconductors are actually multi-step rather than two-step systems. It has been shown that the vitreousness of the microstructure of high-temperature superconductors and the presence of close-packed twin boundaries in samples lead to the penetration of a magnetic flux in the form of hypervortices into the sample and cause the formation of a superconducting glass state on a different physical basis as compared to the Ebner-Stroud model of a granulated glass.     

Quasi-particle excitations around a pair of half-quantum vortices in p- wave superconductors

Triplet superconductors such as Sr₂RuO₄ and Na_xCoO₂⋅yH₂O are now found to be p-wave (p_x ± ip_y) or f-wave ((p_x ± ip_y) cos cp_z) superconductors. It was phenomenologically suggested that in these p-wave or f-wave superconductors, a pair of half-quantum vortices (HQVs) becomes stable. Using the Bogoliubov-de Gennes equation, previously we have analyzed quasi-particle excitations around an HQV at one end of a d-soliton for simplicity. In next study, we will investigate the stability of the pair of HQV’s, which are connected by the d-soliton. For this purpose, we have developed a new numerical method to solve the Bogoliubov-de Gennes equation for two vortices state, using Mathieu functions.     

Surface states and tunneling spectroscopy of high-Tcsuperconductors

Recent studies of high- T_csuperconductors have clarified new aspects of tunneling spectroscopy. The unconventional pairing states, i.e. d-wave symmetry in these materials have been established through various measurements. Differently from isotropic s-wave superconductors, d-wave pairing states have an internal phase of the pair potential. The internal phase modifies the surface states due to the interference effect of the quasiparticles. Along these lines, a novel formula of tunneling spectroscopy has been presented that fully takes into account of the anisotropy of the pair potential. The most essential difference of this formula from conventional ones is that it suggests the phase-sensitive capability of tunneling spectroscopy. The formula suggests that the symmetry of the pair potential is determined by the orientational dependence measurements of tunneling spectroscopy. Along these lines, several experiments have been performed on high-T_c superconductors. The observation of the zero-bias conductance peaks (ZBCP) on Y Ba₂Cu₃O_7 − δstrongly suggests the d_{x² − y²}-wave pairing states of hole-doped high-T_c superconductors. On the other hand, the absence of ZBCP on (electron-doped)Nd_1.85Ce_0.15CuO_4 − δindicates that the pair potential of this material is a nodeless state. In this paper, recent developments of tunneling spectroscopy for anisotropic superconductors are reviewed both on theoretical and experimental aspects.     

Investigation of stimulated dynamics in strongly anisotropic high-temperature superconductors system Bi-Pb-Sr-Ca-Cu-O

It is used the mechanical method of Abrikosov vortex stimulated dynamics investigation in superconductors. With its help it was studied relaxation phenomena in vortex matter of high-temperature superconductors. It established that pulsed magnetic fields change the course of relaxation processes taking place in vortex matter. The study of the influence of magnetic pulses differing by their durations and amplitudes on vortex system of strongly anisotropic high-temperature superconductors system Bi_1.7Pb_0.3Sr₂Ca₂Cu₃O_10−δ showed the presence of threshold phenomena. The small duration pulses do not change the course of relaxation processes taking place in vortex matter. When the duration of pulses exceeds some critical value (threshold), then their influence changes the course of relaxation process which is revealed by stepwise change of relaxing mechanical moment τrel. These investigations showed that the time for formatting of Abrikosov vortex lattice in Bi_1.7Pb_0.3Sr₂Ca₂Cu₃O_10−δ is of the order of 150 μs which on the order of value exceeds the time necessary for formation of a single vortex observed in isotropic high-temperature superconductor HoBa₂Cu₃O_7−δ and on two orders exceeds the creation time of a single vortex observed in classical type II superconductors.     

Critical magnetic field ratio of anisotropic magnetic superconductors

The upper critical field, the lower critical field and the critical magnetic field ratio of anisotropic magnetic superconductors are calculated by Ginzburg–Landau theory analytically. The effect of the Ginzburg–Landau parameter (κ₀), magnetic susceptibility (χ) and magnetic-to-anisotropic parameter ratio (θ) on the critical field ratio are considered. We find that the value of critical field ratio increases with increasing κ₀ and θ, and decreases with increasing χ. The highest and the lowest value of critical field ratio is found in the diamagnetic superconductors and the ferromagnetic superconductors, respectively.     

Nearly frictionless transport of electrons in CuxBi2Se3

We study the electric-field-driven transport of electrons in superconductors (Cu_xBi₂Se₃) by using the borrowed approach which has been successfully adopted to study the critical transport of other superconductors as well as supersolid helium in very low temperature environment. The critical temperatures related to the nearly frictionless transport of electrons were found to be directly relevant to the superconducting temperature of superconductors (Cu_xBi₂Se₃) after selecting specific activation energies.