Pseudogap-state superconductivity in a “hot-point” model: Gor’kov equations

The specific features of the superconducting state (with s and d pairing) are considered in terms of a pseudogap state caused by short-range order fluctuations of the “dielectric” type, namely, antiferromagnetic (spin density wave) or charge density wave fluctuations, in a model of the Fermi surface with “hot points.” A set of recurrent Gor’kov equations is derived with inclusion of all Feynman diagrams of a perturbation expansion in the interaction between an electron and short-range order fluctuations causing strong scattering near hot points. The influence of nonmagnetic impurities on superconductivity in such a pseudogap state is analyzed. The critical temperature for the superconducting transition is determined, and the effect of the effective pseudogap width, correlation length of short-range-order fluctuations, and impurity scattering frequency on the temperature dependence of the energy gap is investigated.     

Suppression of superconductivity in layered Bi<Subscript>4</Subscript>O<Subscript>4</Subscript>S<Subscript>3</Subscript> by Ag doping

We report X-ray diffraction, magnetization and transport measurements for polycrystalline samples of the new layered superconductor Bi_4?x Ag _x O₄S₃(0 ≤ x ≤ 0.2). The superconducting transition temperature (T _C) decreases gradually and finally suppressed when x < 0.10. Accordingly, the resistivity changes from a metallic behavior for x < 0.1 to a semiconductor-like behavior for x > 0.1. The analysis of Seebeck coefficient shows there are two types of electron-like carriers dominate at different temperature regions, indicative of a multiband effect responsible for the transport properties. The suppression of superconductivity and the increased resistivity can be attributed to a shift of the Fermi level to the lower-energy side upon doping, which reduces the density of states at E _F. Further, our result indicates the superconductivity in Bi₄O₄S₃ is intrinsic and the dopant Ag prefers to enter the BiS₂ layers, which may essentially modify the electronic structure.     

Some Features in the behavior of the density of superconducting condensate in superconductors

The correlation between the density ρ_s(T→0) of superconducting condensate and the superconducting transition temperature T _c in underdoped HTSC systems is considered. It is shown that the linear relation between ρ_s(0) and T _c observed in some experiments can easily be interpreted in the framework of the conventional Bardeen-Cooper-Schrieffer (BCS) model without invoking any exotic superconductivity models.     

Temperature dependence of the penetration depth of a magnetic field in the presence of dispersion of the superconducting and charge density wave order parameters

A formula for computing the temperature dependence of the London penetration depth of a magnetic field in the regime of coexistence of charge density waves and superconductivity has been proposed taking into account the dependence of both order parameters on the wave vector. It has been shown that an anomalously high diamagnetic response of the system and a finite value of the superconducting current persist even at T _c ≤ T ≤ T _CDW.     

Theory of dual fermion superconductivity in hole-doped cuprates

Since the discovery of the cuprate high-temperature superconductivity in 1986, a universal phase diagram has been constructed experimentally and numerous theoretical models have been proposed. However, there remains no consensus on the underlying physics thus far. Here, we theoretically investigate the phase diagram of hole-doped cuprates based on an itinerant-localized dual fermion model, with the charge carriers doped on the oxygen sites and localized holes on the copper d _{x2 ? y2} orbitals. We analytically demonstrate that the puzzling anomalous normal state or the strange metal could simply stem from a free Fermi gas of carriers bathing in copper antiferromagnetic spin fluctuations. The short-range high-energy spin excitations also act as the “magnetic glue” of carrier Cooper pairs and induce d-wave superconductivity from the underdoped to overdoped regime, distinctly different from the conventional low-frequency magnetic fluctuation mechanism. We further sketch out the characteristic dome-shaped critical temperature T _c versus doping level. The emergence of the pseudogap is ascribed to the localization of partial carriers coupled to the local copper moments or a crossover from the strange metal to a nodal Kondo-like insulator. Our work provides a consistent theoretical framework to understand the typical phase diagram of hole-doped cuprates and paves a distinct way to the studies of both non-Fermi liquid and unconventional superconductivity in strongly correlated systems.     

Topological electronic transition in cuprate high-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> superconductors occurring before the superconducting transition

It is shown for the first time that the superconducting transition in optimally doped Y- and Bi-based high-T _c superconductors is preceded by the Lifshitz topological transition in their electron systems. A intense hole-electron conversion occurring in the system of charge carriers at T = T _c + (~10 K) is a clear cut signature of such transition.     

Magnetic susceptibility and superconductivity of (Pb<Subscript>0.2</Subscript>Sn<Subscript>0.8</Subscript>)<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>In<Subscript>x</Subscript>Te alloys as a function of in content

Experimental data on the superconductivity of In-doped Pb_zSn_1?zTe alloys (z=0.2) are discussed. The superconducting transition was detected from simultaneous measurements of the resistivity and magnetic susceptibility of a series of samples with different indium contents (2–12 mol % InTe). The superconducting transition detected by the magnetic susceptibility was observed at a temperature which was, on the average, 0.1 K below that determined from the resistivity. The increase in the superconducting transition temperature T _c with increasing indium content is of a threshold character, with T _c being proportional to the inverse electronic density of states at the Fermi level. The observed features in the experimental data are accounted for in terms of indium impurity resonance states in the material.     

On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.     

Phase transitions in hybrid SFS structures with thin superconducting layers

Calculations of critical temperature T _c of the phase transition to superconducting state of a superconductor/ ferromagnet/superconductor (SFS) hybrid structure with proximity effect is performed on the base of linearized Usadel equations. It is shown that the proximity effect between S and F metals and the exchange interaction can induce an inhomogeneous superconducting state with longitudinal to layers Δ _∝ exp(ipz) modulation of the superconductivity order parameter, which is characterized by nonzero value of the wave number p, describing the Larkin–Ovchinnikov–Fulde–Ferrell instability. Influence of this instability on transitions between 0- and π-states of the SFS structure is studied. It is shown that the 0–π transition is accompanied by a nonmonotonic dependence of both the critical temperature T _c and the effective penetration depth Λ of the magnetic field into the hybrid structure on the characteristic size of the ferromagnetic region.     

Robustness of <Emphasis Type="Italic">s</Emphasis>-wave pairing symmetry in iron-based superconductors and its implications for fundamentals of magnetically driven high-temperature superconductivity

Based on the assumption that the superconducting state belongs to a single irreducible representation of lattice symmetry, we propose that the pairing symmetry in all measured iron-based superconductors is generally consistent with the A _1g s-wave. Robust s-wave pairing throughout the different families of iron-based superconductors at different doping regions signals two fundamental principles behind high-T _c superconducting mechanisms: (i) the correspondence principle: the short-range magnetic-exchange interactions and the Fermi surfaces act collaboratively to achieve high-T _c superconductivity and determine pairing symmetries; (ii) the magnetic-selection pairing rule: superconductivity is only induced by the magnetic-exchange couplings from the super-exchange mechanism through cation-anion-cation chemical bonding. These principles explain why unconventional high-T _c superconductivity appears to be such a rare but robust phenomena, with its strict requirements regarding the electronic environment. The results will help us to identify new electronic structures that can support high-T _c superconductivity.     

A brief review on <Emphasis Type="Italic">μ</Emphasis>SR studies of unconventional Fe- and Cr-based superconductors

Muon spin relaxation/rotation (μSR) is a vital technique for probing the superconducting gap structure, pairing symmetry and time reversal symmetry breaking, enabling an understanding of the mechanisms behind the unconventional superconductivity of cuprates and Fe-based high-temperature superconductors, which remain a puzzle. Very recently double layered Fe-based super- conductors having quasi-2D crystal structures and Cr-based superconductors with a quasi-1D structure have drawn considerable attention. Here we present a brief review of the characteristics of a few selected Fe- and Cr-based superconducting materials and highlight some of the major outstanding problems, with an emphasis on the superconducting pairing symmetries of these materials. We focus on μSR studies of the newly discovered superconductors ACa₂Fe₄As₄F₂ (A = K, Rb, and Cs), ThFeAsN, and A₂Cr₃As₃ (A = K, Cs), which were used to determine the superconducting gap structures, the presence of spin fluctuations, and to search for time reversal symmetry breaking in the superconducting states. We also briefly discuss the results of μSR investigations of the superconductivity in hole and electron doped BaFe₂As₂.     

Existence of two types of perfect Bi<Subscript>2</Subscript>Sr<Subscript>2−<Emphasis Type="Italic">x</Emphasis></Subscript>La<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>CuO<Subscript>6+δ</Subscript> single crystals

It is found that perfect Bi₂Sr_2?x La _x CuO_6+δ single crystals with the same concentrations of lanthanum x = 0.64 and excess oxygen δ = 0.237 exist in two types. Single crystals of the first type are obtained by slow cooling (the synthesis time is 90–105 h). They have a monoclinic superlattice and exhibit no superconducting transition down to 2 K. Crystals of the second type are obtained by rapid cooling (the synthesis time is 30–40 h) and are characterized by a orthorhombic superlattice and T _c = 18 K. Thus, the superconducting transition temperature is determined not only by the concentration of carriers but also by the configuration of defects. A rhombic superlattice prevails in single crystals obtained by slow cooling in the lanthanum concentration range x = 0.3–0.5, while a monoclinic superlattice dominates in the range x = 0.75–0.85. This fact explains the high values of T _c at optimal doping (x = 0.4) and the absence of high-T _c superconductivity at p < 0.10.     

Robust superconductivity and transport properties in (Li1-xFex)OHFeSe single crystals

The recently discovered (Li_1-xFe_x)OHFeSe superconductor with T_c about 40 K provides a good platform for investigating the magnetization and electrical transport properties of FeSe-based superconductors. By using a hydrothermal ion-exchange method, we have successfully grown crystals of (Li_1-xFe_x)OHFeSe. X-ray diffraction on the sample shows the single crystalline PbO-type structure with the c-axis preferential orientation. Magnetic susceptibility and resistive measurements show an onset superconducting transition at around T_c=38.3 K. Using the magnetization hysteresis loops and Bean critical state model, a large critical current J_s is observed in low temperature region. The critical current density is suppressed exponentially with increasing magnetic field. Temperature dependencies of resistivity under various currents and fields are measured, revealing a robust superconducting current density and bulk superconductivity.     

The proximity effect in an Fe-Cr-V-Cr-Fe system

The proximity effect was studied in a thin-film Fe-Cr-V-Cr-Fe layered system. As the chromium layer thickness (d_Cr) increases at a fixed thickness of iron layers (d_Fe), the dependence of the superconducting transition temperature (T_c) on d_Cr exhibits a maximum at d_Cr ? 40 Å followed by a sharp decrease. Investigation of the dependence of T_c on d_Fe at a fixed d_Cr showed that the depth of penetration of the Cooper pairs into a chromium layer does not exceed 40 Å. Analysis of the results obtained suggests that, at d_Cr ? 40 Å, chromium layers exhibit the transition from a nonmagnetic state to an incommensurate spin density wave state.     

Conditions for implementation of the superconducting phase of copper oxides with consideration of three-site interactions and spin fluctuations

The concentration dependence of the transition temperature to the superconducting phase is calculated within the t – t' – t" – J* model, which takes into account tree-site interactions. It is shown that the processes of scattering by spin fluctuations qualitatively change the character of the concentration dependences T _c (n). These scattering processes in the normal phase significantly modify the distribution function of Hubbard fermions, determining the pronounced non-Fermi-liquid behavior of the system.     

Exchange and spin-fluctuation mechanisms of superconductivity in cuprates

A microscopic theory of superconductivity is considered in the framework of the Hubbard p-d model for the CuO₂ plane. The Dyson equation is derived in the nonintersecting diagram approximation using the projection technique for the matrix Green function of the Hubbard operator. The solution of the equation for the superconducting gap shows that interband transitions for Hubbard subbands lead to antiferromagnetic exchange pairing as in the t-J model, while intraband transitions additionally lead to spin-fluctuation pairing of the d-wave type. The calculated dependences of the superconducting transition temperature on the hole concentration and of the gap on the wave vector are in qualitative agreement with experiments.     

Enhancement of superconductivity in disordered films by parallel magnetic field

We show that the superconducting transition temperature T _c (H) of a very thin highly disordered film with strong spin-orbital scattering can be increased by a parallel magnetic field H. This effect is due to the polarization of magnetic impurity spins, which reduces the full exchange scattering rate of electrons; the largest effect is predicted for spin-1/2 impurities. Moreover, for some range of magnetic impurity concentrations, the phenomenon of superconductivity induced by magnetic field is predicted: the superconducting transition temperature T _c (H) is found to be nonzero in the range of magnetic fields 0 < H* ≤ H ≤ H _c .     

Low-energy Ce spin excitations in CeFeAsO and CeFeAsO<Subscript>0.84</Subscript>F<Subscript>0.16</Subscript>

We use inelastic neutron scattering to study the low-energy spin excitations of polycrystalline samples of nonsuperconducting CeFeAsO and superconducting CeFeAsO_0.84F_0.16. Two sharp dispersionless modes are found at 0.85 and 1.16 meV in CeFeAsO below the Ce antiferromagnetic (AF) ordering temperature of T _N ^Ce ? 4 K. On warming to above T _N ^Ce ? 4 K, these two modes become one broad dispersionless mode that disappears just above the Fe ordering temperature T _N ^Fe ? 140 K. For superconducting CeFeAsO_0.84F_0.16, where Fe static AF order is suppressed, we find a weakly dispersive mode center at 0.4 meV that may arise from short-range Ce-Ce exchange interactions. Using a Heisenberg model, we simulate powder-averaged Ce spin wave excitations. Our results show that we need both Ce spin wave and crystal electric field excitations to account for the whole spectra of low-energy spin excitations.     

Topology of the Fermi surface and the coexistence of orbital antiferromagnetism and superconductivity in cuprates

It has been shown that the strong coupling model taking into account a rise in the spin antiferromagnetic insulating state explains the doping dependence of the topology and shape of the Fermi contour of superconducting cuprates. Hole pockets with shadow bands in the second Brillouin zone form the Fermi contour with perfect ordinary and mirror nesting, which ensures the coexistence of orbital antiferromagnetism and superconductivity with a large pair momentum for T < T_C. The weak pseudogap region (T_* < T < T*) corresponds to the orbital antiferromagnetic ordering, which coexists with the incoherent state of superconducting pairs with large momenta in the strong pseudogap region (T_C < T < T_*).     

The electron energy spectrum and superconducting transition temperature of strongly correlated fermions with three-center interactions

The renormalizations of the fermionic spectrum are considered within the framework of the t-J* model taking into account three-center interactions (H₍₃₎) and magnetic fluctuations. Self-consistent spin dynamics equations for strongly correlated fermions with three-center interactions were obtained to calculate quasi-spin correlators. A numerical self-consistent solution to a system of ten equations was obtained to show that, in the nearest-neighbor approximation, simultaneously including H₍₃₎ and magnetic fluctuations at n>n₁ (n₁ ≈ 0.72 for 2t/U = 0.25) caused qualitative changes in the structure of the energy spectrum. A new Van Hove singularity is then induced in the density of states, and an additional maximum appears in the T_c(n) concentration dependence of the temperature of the transition to the superconducting phase with order parameter symmetry of the d _x ²?y² type.