Five-fold way to new high <Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> superconductors

Discovery of high T _c superconductivity in La_2?x Ba _x CuO₄ by Bednorz and Muller in 1986 was a breakthrough in the 75-year long search for new superconductors. Since then new high T _c superconductors, not involving copper, have also been discovered. Superconductivity in cuprates also inspired resonating valence bond (RVB) mechanism of superconductivity. In turn, RVB theory provided a new hope for finding new superconductors through a novel electronic mechanism. This article first reviews an electron correlation-based RVB mechanism and our own application of these ideas to some new noncuprate superconducting families. In the process we abstract, using available phenomenology and RVB theory, that there are five directions to search for new high T _c superconductors. We call them five-fold way. As the paths are reasonably exclusive and well-defined, they provide more guided opportunities, than before, for discovering new superconductors. The five-fold ways are (i) copper route, (ii) pressure route, (iii) diamond route, (iv) graphene route and (v) double RVB route. Copper route is the doped spin-½ Mott insulator route. In this route one synthesizes new spin-½ Mott insulators and dopes them chemically. In pressure route, doping is not external, but internal, a (chemical or external) pressure-induced self-doping suggested by organic ET-salts. In the diamond route we are inspired by superconductivity in boron-doped diamond and our theory. Here one creates impurity band Mott insulators in a band insulator template that enables superconductivity. Graphene route follows from our recent suggestion of superconductivity in doped graphene, a two-dimensional broadband metal with moderate electron correlations, compared to cuprates. Double RVB route follows from our recent theory of doped spin-1 Mott insulator for superconductivity in iron pnictide family.     

Superconductivity in impurity bands

We present a theory of superconductivity in doped insulators. In the magnetic metal state of the compound we obtain the self-consistency equations for the superconducting state in the spin-dependent impurity bands of both extended and localized states in the initial insulator gap. A BCS-type triplet pairing field is considered. We show that the superconducting gap in which single-electron extended states do not exist is overlapped by the distribution of the localized states. The formation of a latent superconducting gap is discussed in connection with the unusual properties of high-T _c compounds. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 419–424 (10 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Generalizing the Cooper-pair instability to doped Mott insulators

Copper oxides become superconductors rapidly upon doping with electron holes, suggesting a fundamental pairing instability. The Cooper mechanism explains normal superconductivity as an instability of a fermi-liquid state, but high-temperature superconductors derive from a Mott-insulator normal state, not a fermi liquid. We show that precocity to pair condensation with doping is a natural property of competing antiferromagnetism and d-wave superconductivity on a singly-occupied lattice, thus generalizing the Cooper instability to doped Mott insulators, with significant implications for the high-temperature superconducting mechanism.     

Doping dependence of Meissner effect in cuprate superconductors

Within the t–t′–J model, the doping dependence of the Meissner effect in cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. Following the linear response theory, it is shown that the electromagnetic response consists of two parts, the diamagnetic current and the paramagnetic current, which exactly cancels the diamagnetic term in the normal state, and then the Meissner effect is obtained for all the temperature T ? T_c throughout the superconducting dome. By considering the two-dimensional geometry of cuprate superconductors within the specular reflection model, the main features of the doping and temperature dependence of the local magnetic field profile, the magnetic field penetration depth, and the superfluid density observed on cuprate superconductors are well reproduced. In particular, it is shown that in analogy to the domelike shape of the doping dependent superconducting transition temperature, the maximal superfluid density occurs around the critical doping δ ≈ 0.195, and then decreases in both lower doped and higher doped regimes.     

Possible propagation of the Zhang-Rice singlet as a probable Cooper channel in the CuO2 planes

The issue of how superconductivity originate in the CuO₂ planes believed to be crucial to understanding the high Tc superconducting cuprates is still an going debate. In the wake of recent experimental observations of the Zhang-Rice singlet (ZRS), its formation and propagation need to be revisited especially by using a simple approach almost at a phenomenological level. Within a highly simplified correlated variational approach (HSCVA) in this Letter, a new formation of the ZRS as constituting the ground state of a single-band t-J model of the CuO₂ planes is developed. This formation is then used to demonstrate how the ZRS can be propagated as a probable Cooper channel in the CuO₂ planes.     

Scanning tunneling spectroscopy of a superlattice superconductor: Bi2Sr2CaCu2O8

It is clear that many of the cuprate superconductors are truly superlattices, composed of sheets whose individual superconducting critical temperatures may approach bulk values. Such a cuprate is Bi₂Sr₂CaCu₂O₈, often referred to as BSCCO-2212. Scanning tunneling spectroscopy (vacuum tunneling) applied toa-bBiO cleavage planes ofT_c≈90 K BSCCO single crystals under liquid helium simultaneously provides topography and local dI/dVspectra (superconducting density of states: DOS). The spectra, which are similar to those obtained from angle-resolved photoemission spectroscopy, confirm a large gap parameter Δ(x,y) on the uppermost layer. The dI/dVspectra do not unequivocally select order parameter symmetry, but are probably consistent with d-wave or anisotropic s-wave states. Spatial variations of Δ on a 100 Å scale are attributed to variation in BiO metallicity, originating in oxygen stoichiometry variations. A model is presented to explain the different dI/dVspectra which are seen, and associated with different local oxygen concentrations. This model, based on the superconducting proximity effect, assumes that in some regions the BiO uppermost layer is insulating and in other regions it is metallic, in the latter case induced superconductivity by proximity to the CuO₂planes. Our STM measurements appear to sample only the uppermost half cell of the crystal, and contain no obvious superlattice features. Recent measurements have confirmed Josephson radiation from voltage biasedc-axis pillars of BSCCO. From the point of view of the present work, the superconducting systems which weakly couple along thec-direction to create Josephson junctions are probably half-cell slabs of height 15.4 Å, each containing two CuO₂and two BiO layers, which act as single composite electrodes for the Josephson junctions.     

Effect of the nanoscale structural inhomogeneity on the magnetic and superconducting characteristics of fine-grained YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> HTSCs

It has been experimentally established that the nanoscale structural inhomogeneity, inherent in fine-grained (0.4 ≤ 〈D〉 ≤ 2μm) high-temperature superconductors YBa₂Cu₃O _y (y ≈ 6.92, T _C ≈ 92 K) and manifesting itself in partial interplane redistribution of oxygen [1, 2], changes the density of states near the Fermi level and decreases the coherence length and density of superconducting carriers in CuO₂ planes. The revealed relationship between the changes in these characteristics with respect to their equilibrium values corresponds to the relationship that might occur for conventional superconductors.     

Generalizing the Cooper-pair instability to doped Mott insulators

Copper oxides become superconductors rapidly upon doping with electron holes, suggesting a fundamental pairing instability. The Cooper mechanism explains normal superconductivity as an instability of a fermi-liquid state, but high-temperature superconductors derive from a Mott-insulator normal state, not a fermi liquid. We show that precocity to pair condensation with doping is a natural property of competing antiferromagnetism and d-wave superconductivity on a singly-occupied lattice, thus generalizing the Cooper instability to doped Mott insulators, with significant implications for the high-temperature superconducting mechanism.     

The Kohn-Luttinger effect and anomalous pairing in new superconducting systems and graphene

We present a review of theoretical investigations into the Kohn-Luttinger nonphonon superconductivity mechanism in various 3D and 2D repulsive electron systems described by the Fermi-gas, Hubbard, and Shubin-Vonsovsky models. Phase diagrams of the superconducting state are considered, including regions of anomalous s-, p-, and d-wave pairing. The possibility of a strong increase in the superconducting transition temperature T _c even for a low electron density is demonstrated by analyzing the spin-polarized case or the two-band situation. The Kohn-Luttinger theory explains or predicts superconductivity in various materials such as heterostructures and semimetals, superlattices and dichalcogenides, high-T _c superconductors and heavy-fermion systems, layered organic superconductors, and ultracold Fermi gases in magnetic traps. This theory also describes the anomalous electron transport and peculiar polaron effects in the normal state of these systems. The theory can be useful for explaining the origin of superconductivity and orbital currents (chiral anomaly) in systems with the Dirac spectrum of electrons, including superfluid ³He-A, doped graphene, and topological superconductors.     

Coulomb repulsion-induced hyperbolic pairing as a mechanism of high-T c superconductivity

The hyperbolic metric of the dispersion law (the effective mass tensor components of carriers are opposite in sign) in the vicinity of the Fermi contour in high-T _c superconducting cuprates in the case of repulsive interaction gives rise to a superconducting state characterized by the condensate of pairs with a large total momentum (hyperbolic pairing). The gain in the energy of the superconducting state over the normal state is due to the fact that a change in the kinetic energy of pairs (because of the negative light component of the effective mass) dominates over the change in the potential energy (corresponding to energy loss). The shift of the chemical potential upon the transition to the superconducting phase is substantial in this case. With increasing repulsive interaction, the superconducting gap δ_K increases and the resulting gain in energy changes to an energy loss at a certain critical value of the repulsive potential. The low temperature T _c of the superconducting transition and the large value of δ _K in this region of potential values are the reasons for the high value of the 2δ_K/T _c ratio and for the developed quantum fluctuations that are observed in underdoped cuprate superconductors.     

Quantum-well structured high-Tc superconductors prepared by soft-chemical method

We have synthesized quantum-well structured high-T_c superconductors through soft-chemical processes, where Bi-based cuprate lattices are regularly interstratified with atom, molecule, and ionic salt. In these materials, superconducting (S) and nonsuperconducting (I) layers are alternately stacked to form superlattices with atomically clear-cut interfaces between them. The intercalation technique, which means a reaction of incorporating chemical species (guest) into the pre-synthesized layered compound (host), could provides an easy route to superconducting superlattices with molecular-level layer-by-layer structural feature. The joint analysis of temperature-dependent magnetic susceptibilities and X-ray absorption spectroscopy indicated that superconducting transition temperature is predominantly governed by the electronic structure of superconductive CuO₂ plane.     

Advances on topological materials

We review application of the SU(4) model of strongly-correlated electrons to cuprate and iron-based superconductors. A minimal self-consistent generalization of BCS theory to incorporate antiferromagnetism on an equal footing with pairing and strong Coulomb repulsion is found to account systematically for the major features of high-temperature superconductivity, with microscopic details of the parent compounds entering only parametrically. This provides a systematic procedure to separate essential from peripheral, suggesting that many features exhibited by the high-T_c data set are of interest in their own right but are not central to the superconducting mechanism. More generally, we propose that the surprisingly broad range of conventional and unconventional superconducting and superfluid behavior observed across many fields of physics results from the systematic appearance of similar algebraic structures for the emergent effective Hamiltonians, even though the microscopic Hamiltonians of the corresponding parent states may differ radically from each other.

     

Muon spin rotation in GdSr2Cu2RuO8: Implications

Muon spin rotation measurements are reported for GdSr₂Cu₂RuO₈, a material with an onset temperature for superconductivity of about 45 K (which is virtually the same for its superconducting sister compounds Sr₂YRu_{1? u} Cu _u O₆ and Gd_{2? z} Ce _z Sr₂Cu₂RuO₁₀). The data indicate two magnetic ordering transitions, at about 15 K and about 130 K, in addition to the Gd ordering transition known to occur at about 2.6 K. We tentatively attribute the 130 K transition to Ru and the 15 K transition to Cu ordering, effectively ruling out any superconducting mechanism based on fluctuating magnetic moments, which are frozen below about 15 K. If there is only one mechanism of high-temperature superconductivity, then the three facts that (i) all three sister compounds have essentially the same onset T _c for superconductivity and (ii) all three of these compounds contain SrO layers but (iii) only two of the three compounds, GdSr₂Cu₂RuO₈ and Gd_{2? z} Ce _z Sr₂Cu₂RuO₁₀ (and not Sr₂YRu_{1? u} Cu _u O₆) contain cuprate planes imply that the superconducting layers of all three compounds must be the common SrO layers, and not the cuprate planes (which do not occur in Cu-doped Sr₂YRuO₆). Otherwise the coincidence of onset temperatures must be an accident, and there must be at least two mechanisms of high-T _c superconductivity: one for doped Sr₂YRuO₆ and another for cuprate-plane superconductivity.     

A model for layered high-temperature superconductors with two CuO2 layers per unit cell

We extend a model for layered high-temperature superconductors to systems with two CuO₂ layers per unit cell and two interlayer spacings with different physical properties. The carriers are assumed to occupy Fermi liquid states, forming narrow tight-binding bands. The layers are coupled by weak interlayer-hopping matrix elements between adjacent sheets, as well as by an attractive interaction between carriers in neighboring layers in addition to an on-site intralayer coupling. We solve the Gorkov equations for this model to obtain the critical temperature and the density of states of the oneparticle excitations from the superconducting condensate, and discuss various parameter regimes concerning the coupling between the two layers. We compare our results with current experimental findings for high-temperature superconductors. The presence of two CuO₂ layers leads to multi-peak features in the superconducting density of states, as has been observed in recent tunneling measurements.     

Atomic structure and diffusion properties of superanisotropic diffusive systems

The diffusion of oxygen tracer atoms has is, and a diffusion-structural analysis is made of the oxygen subsystem of the Sr_2.4Ca_1.6Bi₂O_8.8 oxide representing a copper-free precursor of bismuth high-T _c superconductors. The diffusion in this compound has been shown to be superanisotropic. It has been established that superanisotropic diffusion in the oxygen subsystem of oxide systems, rather than being connected with the high-temperature superconductivity and the existence of CuO₂ planes, is accounted for by the general features of their crystal structure.     

Magnetic resonance of Cu and of Gd in insulating GdSr<Subscript>2</Subscript>Cu<Subscript>2</Subscript>NbO<Subscript>8</Subscript> and in superconducting GdSr<Subscript>2</Subscript>Cu<Subscript>2</Subscript>RuO<Subscript>8</Subscript>

Weak-ferromagnetic (or antiferromagnetic) resonance of Cu and electron spin resonance (ESR) of Gd are observed both in insulating GdSr₂Cu₂NbO₈ and in superconducting GdSr₂Cu₂RuO₈. The Cu resonance implies that the CuO₂ planes are magnetic and indicates that the superconducting layer of GdSr₂Cu₂RuO₈ is SrO (not CuO₂), as in its related superconducting compound without cuprate planes, doped Sr₂YRuO₆.     

The vortex-like excitations detected by Nernst signals in high-Tc 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.     

The anomalous anisotropy in the ac susceptibility of La1.45Nd0.4Sr0.15CuO4 single crystal

The dependencies of ac susceptibility on the superimposed dc magnetic fields for the stripe-ordered La_1.45Nd_0.4Sr_0.15CuO₄ single crystal with two superconducting transitions have been studied in the 3D and 2D superconducting ranges for the fields along different orientations of the crystal. The results show that with increasing fields the interlayer Josephson coupling and the in-plane superconductivity are suppressed orderly for the fields perpendicular to CuO₂ planes. The influences of the field parallel to CuO₂ planes on the 3D and 2D superconductivity are much weaker than those of the field parallel to the c-axis. The irreversibility lines for the 3D and 2D superconducting states are also studied.     

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.