Islands of stability of the d-wave order parameter in s-wave anisotropic superconductors

In this paper we find and present on diagrams in the coordinates of η=2t₁/t₀ (the ratio of the second and the first nearest neighbor hopping integrals) and n (the carrier concentration) the areas of stability for the superconducting spin-singlet s- and d-wave and the spin-triplet p-wave order parameters hatching out during the phase transition from the normal to the superconducting phase. The diagrams are obtained for an anisotropic two-dimensional superconducting system with a relatively wide partially-filled conduction band. We study a tight-binding model with an attractive nearest neighbor interaction with the amplitude V₁, and the on-site interaction (with the amplitude V₀) taken either as repulsive or attractive. The problem of the coexistence of the s-, p- and d-wave order parameters is addressed and solved for chosen values of the ratio V₀/V₁. A possible island of stability of the d-wave order parameter in the s-wave order parameter environment for a relatively strong on-site interaction is revealed. The triple points, around which the s-, d-, and p-wave order parameters coexist, are localized on diagrams. It is shown that results of the calculations performed for the two-dimensional tight-binding band model are dissimilar with some obtained within the BCS-type approximation.     

非中心对称超导序参量研究

非中心对称超导体是近年发现的一类新型超导材料. 在这类材料中, 非中心对称的晶体势场产生一个有效的反对称自旋-轨道耦合(ASOC)并导致自旋简并的能级发生分裂, 从而在超导配对态中允许自旋单态和自旋三重态混合. 这一性质有别于先前研究的大部分超导体, 需要从概念上突破BCS理论框架. 此外, 理论研究还表明非中心对称超导可能还是一类潜在的拓扑超导材料. 这些独特的物理性质已激发了广泛的研究兴趣, 并且越来越受到关注.#br#超导序参量的对称性是认识和理解超导形成机理的一个重要物理量. 本文将介绍基于隧道二极管的伦敦穿透深度测量技术, 并简要综述非中心对称超导的研究现状以及穿透深度测量在非中心对称超导序参量研究中的应用. 通过对比研究具有不同反对称自旋-轨道耦合强度的非中心对称超导材料, 我们发现其混合超导配对态与反对称自旋-轨道耦合强度缺乏简单的对应关系, 但与能带劈裂(E_ASOC)相对于超导转变温度(T_c)的比值(E_r=E_ASOC/T_c)紧密相关.     

Theory of the spin-triplet superconductivity in Sr2RuO4 based on perturbation approach to three-band Hubbard model

We investigate a mechanism of the spin-triplet superconductivity in Sr₂RuO₄ by solving Eliashberg equation for three-band Hubbard model, where the effective pairing interaction is expanded perturbatively up to the third order with respect to the Coulomb integrals and the transition temperature is estimated numerically. The most significant momentum dependence of the effective interaction for the spin-triplet p-wave superconductivity does not originate from that of the spin susceptibility, but is brought by the third order vertex corrections. The results show that the p-wave pairing state is stabilized for not so strong inter-orbit couplings.     

Sign reversal of the order parameter near <Emphasis Type="Italic">s</Emphasis><Subscript>±</Subscript>-superconductor surface

The superconducting order parameter and LDOS spectra near an impenetrable surface are studied on the basis of self-consistent calculations for a two band superconductor with nodeless extended s-wave order parameter symmetry, as possibly realized in Fe-based high-temperature superconductors. It is found that for a wide range of parameters the spatial behavior of the order parameter at a surface is not reduced to a trivial suppression. If the interband scattering at a surface is of the order of the intraband one or dominates it, it can be energetically favorable to change the symmetry of the superconducting state near the surface from s _± to conventional s-wave. The range of existing of this surface conventional superconductivity is very sensitive to the relative values of interband and intraband pairing potentials. It is shown that the LDOS spectra near the surface can qualitatively differ upon calculating with and without taking into account the self-consistency of the order parameter.     

Pairing symmetry in layered BiS2 compounds driven by electron-electron correlation

We investigate the pairing symmetry of layered BiS2 compomlds by assuming that electron-electron correlation is still important so that the pairing is rather short range. We lind that the extended .s-wave pairing symmetry always wins over d-wave when the pairing is confined between two short range sites up to next nearest neighbors. The pairing strength is peaked around the doping level ：r = 0.5. which is consistent with experimental observation. The extended s-wave pairing symmetry is very robust against spin orbital coupling because it is mainly determined by the structure of Fermi surfaces, Moreover. the extended s-wave pafiring can be distinguished from conventional swave pairing by measuring and comparing superconducting gaps of different Fermi surfaces.     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Phase-sensitive tests of the pairing state symmetry in Sr(2)RuO(4)

Exotic superconducting properties of have provided strong support for an unconventional pairing symmetry. However, the extensive efforts over the past decade have not yet unambiguously resolved the controversy about the pairing symmetry in this material. While recent phase-sensitive experiments using flux modulation in Josephson junctions consisting of and a conventional superconductor have been interpreted as conclusive evidence for a chiral spin-triplet pairing, we propose here an alternative interpretation. We show that an overlooked chiral spin-singlet pairing is also compatible with the observed phase shifts in Josephson junctions and propose further experiments which would distinguish it from its spin-triplet counterpart.     

Odd-frequency pairings in a non-centrosymmetric system

We study possible pairing symmetries of non-centrosymmetric superconductors in the Hubbard model with the Rashba-type spin–orbit interaction (RSOI). Because of the breakdown of space inversion symmetry due to RSOI, a mixture of pairing states with different symmetries can emerge. We find that the RSOI mixes not only the spin-singlet even-parity pairing and spin-triplet odd-parity pairings with even-frequency symmetry, but it also mixes the spin-singlet odd-parity pairing and spin-triplet even-parity pairings with odd-frequency symmetry.     

Applications of the conformal transformation method in studies of composed superconducting systems

A framework for analytical studies of superconducting systems is presented and illustrated. The formalism, based on the conformal transformation of momentum space, allows one to study the effects of both the dispersion relation and the structure of the pairing interaction in two-dimensional anisotropic high-T _c superconductors. In this method, the number of employed degrees of freedom coincides with the dimension of the momentum space, which is different compared to that in the standard Van Hove scenario with a single degree of freedom. A new function, the kernel of the density of states, is defined and its relation to the standard density of states is explained. The versatility of the method is illustrated by analyzing coexistence and competition between spin-singlet and spin-triplet order parameters in superconducting systems with a tight-binding-type dispersion relation and an anisotropic pairing potential. Phase diagrams of stable superconducting states in the coordinates η (the ratio of hopping parameters) and n (the carrier concentration) are presented and discussed. Moreover, the role of attractive and repulsive on-site interactions for the stability of the s-wave order parameter is explained.     

Coulomb repul sion of hole s and competition between $${d_{{x^2} - {y^2}}}$$ -wave and s-wave paring s in cuprate superconductor s

The effect of the Coulomb repulsion of holes on the Cooper instability in an ensemble of spin–polaron quasiparticles has been analyzed, taking into account the peculiarities of the crystallographic structure of the CuO₂ plane, which are associated with the presence of two oxygen ions and one copper ion in the unit cell, as well as the strong spin–fermion coupling. The investigation of the possibility of implementation of superconducting phases with d-wave and s-wave of the order parameter symmetry has shown that in the entire doping region only the d-wave pairing satisfies the self-consistency equations, while there is no solution for the s-wave pairing. This result completely corresponds to the experimental data on cuprate HTSC. It has been demonstrated analytically that the intersite Coulomb interaction does not affect the superconducting d-wave pairing, because its Fourier transform V _q does not appear in the kernel of the corresponding integral equation.     

Electronic structure and superconductivity of κ-(BEDT-TTF)2X salts

We have analyzed the electronic structure and superconducting properties of layered crystals based on BEDT-TTF salts (hereafter denoted as ET), in which intramolecular interaction among electrons is important. For the case of realistic κ-packing of ET-molecules in a plane of ET₂ dimers we have calculated the electron density of states. Using the calculated electronic structure, we have analyzed the symmetry of the anisotropic superconducting pairing. The critical value of the effective attraction between electrons for formation of a bound pair in an empty lattice has been estimated. The relation between the nodes of the d-type order parameter on the anisotropic Fermi surface and superconducting properties of the condensate is discussed in the Bardeen-Cooper-Schrieffer (BCS) model. The results are in agreement with the known band parameters of the normal phase and measurements of the magnetic field penetration depth, heat capacity as a function of temperature in the low-temperature range, and NMR in κ-ET₂X superconducting salts. Zh. éksp. Teor. Fiz. 113, 715–733 (February 1998)     

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t = - 0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder. Received 23 January 2002     

Theory of the proximity effect in junctions with unconventional superconductors

We present a general theory of the proximity effect in junctions between diffusive normal metals (DN) and superconductors. Various possible symmetry classes in a superconductor are considered: even-frequency spin-singlet even-parity (ESE) state, even-frequency spin-triplet odd-parity state, odd-frequency spin-triplet even-parity (OTE) state and odd-frequency spin-singlet odd-parity state. It is shown that the pair amplitude in a DN belongs, respectively, to an ESE, OTE, OTE, and ESE pairing state since only the even-parity s-wave pairing is possible due to the impurity scattering.     

Short-range spin correlations and pseudogap in underdoped cuprates

In this paper we show that local spin-singlet amplitude with d-wave symmetry can be induced by short-range spin correlations even in the absence of pairing interactions. In the present scenario for the pseudogap, the normal state pseudogap is caused by the induced local spin-singlet amplitude due to short-range spin correlations, which compete in the low energy sector with superconducting correlations to make T_c go to zero near half-filling.     

Chiral superconducting phase transition in 3-K phase of Sr2RuO4

We have investigated the transports of micro-fabricated sample of 3-K phase superconductivity (T_c  3 K) in Sr₂RuO₄–Ru eutectic system in order to clarify the pairing symmetry. Up to now, pure Sr₂RuO₄ (T_c = 1.5 K: 1.5-K phase) is widely recognized to be a spin-triplet odd-parity superconductor. However, the enhancement mechanism of T_c up to 3 K and the pairing symmetry of the 3-K phase have not been cleared yet. By using micro fabrication technique with focused ion beam, we have succeeded to extract individual superconducting channels for the 3-K phase in which only a few pieces of Ru inclusions are contained. Multiple kink structures observed in differential resistance–current (dV/dI − I) characteristics indicate serially connected superconducting filaments in the 3-K phase. We confirm that the 3-K phase is an odd-parity superconductor similar to pure Sr₂RuO₄ from the monotonous temperature dependence of the critical currents. In addition, we observed a quite unusual hysteresis in dV/dI − I below 2 K, which suggests the internal degrees of freedom in the superconducting state: the most probably the chiral p-wave state.     

Odd-frequency superconductivity on the Hubbard model using the FLEX approximation

It is an important issue to clarify whether the odd-frequency superconducting state can be derived from microscopic Hamiltonian or not, where gap function has an odd-parity in frequency. We study the instability of following four superconducting states: (1) even-frequency spin-singlet, (2) even-frequency spin-triplet, (3) odd-frequency spin-singlet and (4) odd-frequency spin-triplet. By using the fluctuation exchange (FLEX) approximation on a triangular and square lattice, we find that the odd-frequency spin-triplet pairing can become dominant at a certain region where the suppression of the antiferromagnetic fluctuation due to a geometric frustration becomes prominent.     

Mixed spin-singlet and spin-triplet cooper pairing caused by inhomogeneous magnetism

With an attractive electron-electron interaction only for spin-singlet Cooper pairing and in the presence of inhomogeneous magnetism, spin-singlet and spin-triplet pair amplitudes both occur when only a spin-singlet pair potential occurs. Pair amplitudes in $\text{k}$-space and $\text{r}$-space and the spin susceptibility show that superconductivity in the presence of inhomogeneous magnetism cannot be either purely spin-singlet or purely spin-triplet pairing.     

Electronic properties of nano-structured anisotropic superconductors

Using the Bogoliubov-de Gennes equation on the tight-binding electron model, we have investigated nano-structured anisotropic superconductors. For a π/4-rotated square d-wave superconducting plate, the superconducting symmetry becomes s+id, not only at the surfaces, but over the whole superconductor. Also we have investigated quasi-particle structures of this superconducting state.     

Spin-switch effect in a graphene d-wave superconductor spin-valve

In this paper, spin-switch effect under the influence of anisotropic pairing symmetry is investigated. It is shown that the non-local conductance is sensitive to the exchange splitting, the incident energy, and the orientation of the superconducting gap. With the increase of the exchange splitting from zero to Fermi energy, the crossed Andreev reflection conductance for parallel configuration of magnetization and the elastic co-tunneling conductance for antiparallel configuration of magnetization are suppressed to a vanishing value. When the exchange splitting equates to Fermi energy, for values of the orientation of d-wave superconducting gap in the k-space very close to π / 4, magnitude of the spin-switch effect is suppressed completely. Moreover, in contrast to the single graphene-based ferromagnet/superconductor junction case, a π / 2 periodic oscillatory behavior about the barrier is observed directly in the present spin valve. The physical origination for those phenomena has also been analyzed.