Are the high Tc superconductors d-wave?

Although it has been widely accepted for several years that the normal state of high T_c superconductors is anomalous, only recently has there been growing evidence for the anomalous nature of the superconducting state. A number of recent experiments show clear evidence for the existence of low-lying excitations in the superconducting state. Moreover, the observation by Bonn, Hardy and coworkers of a linear temperature dependence in the microwave surface resistance and penetration depth of YBCO at low temperatures suggests d-wave pairing with line nodes. The evidence for and against unconventional superconductivity in the high T_c oxides is reviewed. Specific topics discussed include the different behaviours observed for the penetration depth in thin films and in single crystals, what is known about the absolute value of the penetration depth, the role of disorder and inelastic scattering, the relative merits of strongvs. weak correlation theories of d-wave superconductivity in the high T_c oxides, and most important, what have we actually learned about the penetration depth of high T_c superconductors fromμSR?     

Pseudogap phenomena in ultracold atomic Fermi gases

The pairing and superfluid phenomena in a two-component ultracold atomic Fermi gas is an analogue of Cooper pairing and superconductivity in an electron system, in particular, the high Tc superconductors. Owing to the various tunable parameters that have been made accessible experimentally in recent years, atomic Fermi gases can be explored as a prototype or quantum sinmlator of superconductors. It is hoped that, utilizing such an analogy, the study of atomic Fermi gases may shed light to the mysteries of high Tc superconductivity. One obstacle to the ultimate understand- ing of high Tc superconductivity, from day one of its discovery, is the anomalous yet widespread pseudogap phenomena, for which a consensus is yet to be reached within the physics comnnmity, after over 27 years of intensive research efforts. In this article, we shall review the progress in the study of pseudogap phenomena in atomic Fermi gases in terms of both theoretical understanding and experimental observations. We show that there is strong, unambiguous evidence for the existence of a pseudogap in strongly interacting Fermi gases. In this context, we shall present a pairing fuctuation theory of the pseudogap physics and show that it is indeed a strong candidate theory for high Tc superconductivity.     

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.     

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.     

Workshop on fast structural changes

Copper-oxide (cuprate) high-temperature superconductors are doped Mott insulators. The undoped parent compounds are antiferromagnetic insulators, and superconductivity occurs only when an appropriate number of charge carriers (electrons or holes) are introduced by doping. All cuprate materials contain CuO₂ planes (Figure 1a) in their crystal structure; the doped carriers are believed to go into these CuO₂ planes, which are responsible for high-temperature superconductivity. High-temperature superconductors are characterized by their unusual physical properties, both in the superconducting state (below the superconducting transition temperature T_c) and in the normal state (above T_c). Since the discovery of high-temperature superconductivity in 1986 [1], these unusual physical properties and the mechanism of superconductivity have been prominent issues in condensed matter physics [2].     

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.     

Quasiparticles in a strongly correlated liquid with the fermion condensate: applications to high-temperature superconductors

A model of a strongly correlated electron liquid based on fermion condensation (FC) is extended to high-temperature superconductors. Within our model, the appearance of FC presents a boundary separating the region of a strongly interacting electron liquid from the region of a strongly correlated electron liquid. We study the superconductivity of a strongly correlated liquid and show that, under certain conditions, the superconductivity vanishes at temperatures T > T _c ≈ T _node, with the superconducting gap being smoothly transformed into a pseudogap. As a result, the pseudogap occupies only a part of the Fermi surface. The gapped area shrinks with increasing the temperature and vanishes at T = _T*. The single-particle excitation width is also studied. The quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by the effective masses and, intersecting near the binding energy that is on the order of the superconducting gap. It is argued that this strong change of the quasiparticle dispersion upon binding can be enhanced in underdoped samples because of strengthening the FC influence. The FC phase transition in the presence of the superconductivity is examined, and it is shown that this phase transition can be considered as driven by the kinetic energy.     

“Magnetodipole” self-organization of charge carriers in high-T c superconductors and the kinetics of phase transition

A phenomenological model describing “magnetodipole” self-organization of charge carriers (the formation of so-called stripe-structures and the energy gap in the spectrum of states) was suggested to interpret the data of nonstationary nonlinear spectroscopy of high-T _c superconductors. It was shown that, after rapidly heating a superconducting sample, the kinetics of the succeeding phase transition depended on initial temperature T. At small “overheatings” T*<T<T _m x≈(1.4?1.5)T* (T _c and T*≈T _c are the temperatures of the transition to the superconducting state and the formation of stripe-structures) and the optimal level of doping, the decay of stripe-structures (and of the gap in the spectrum of states) occurred at a low rate (in times above to 10^?9 s) in spite of the virtually instantaneous disappearance of superconductivity.     

Another approach to mechanism of ferromagnetic superconductor UGe2

We study the ferromagnetic superconductor of UGe₂ applying our previous model [Phys. Rev. B 61 (2000), 4289] for the high transition temperature superconductivity (HTSC). The Coulomb interaction for triplet electron pairs is reduced by a difference of the exchange interaction. In the case of UGe₂ including other heavy fermion superconductors, coexistence of triplet superconductivity and ferromagnetism is possible in the case of our scheme. We also investigate the pressure-dependence of Curie temperature, T_c and superconducting temperature, T_sc.     

On the limits of consistency of Eliashberg theory and the density of states of high-T c superconductors

We make a detailed study of the Eliashberg theory in the coupling region where some fundamental qualitative deviations from the conventional BCS-like behavior begin to appear. These deviations are identified as the onset of a cross-over from BCS superconductivity to Bose condensation. We point out that the beginning of this cross-over occurs when the gap δ _g becomes comparable to the boson energies Ω_ph. This condition traduces the physical constraint that the distance the paired electron covers during the absorption of the virtual boson, cannot be larger than the coherence length. The frontier region of couplings is of the order of λ ≈ 3, and high-T _c, materials are concerned. A clear qualitative indication of the occurrence of a crossover regime should be a dip structure above the gap in the density of states of excitations, and this is one of the most robust characteristics of the high-T _c, superconducting state. Comparing our results with tunneling and photoemission experiments we conclude that high-T _c materials (cuprates and fullerides) are indeed at the beginning of a cross-over from BCS superconductivity to Bose condensation, even though the fermionic nature still prevails. If the Uemura plot is relevant, then the dip should also be present in the other materials that are close to the cross-over regime like heavy Fermion and organic superconductors. In all these materials Ginzburg Landau equations are irrelevant.     

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.     

Coherent state and superconductivity in the free carrier-bipolaron interacting system

In this paper a model to describe the free carrier-bipolaron interacting system is proposed. Effective hopping of the bipolaron is studied in the slave-boson approach, and a characteristic temperature T¹ is obtained, below which the system enters a coherent state. The density of states in the normal state and the superconductivity of the system are discussed in a quasiparticle picture. The results show that the mixing between the free carrier and the bipolaron results in an enhancement of the effective mass of the quasiparticle and meanwhile the renormalized coupling interaction, arising from the negative correlation energy in the bipolaron region, enhances the effective superconducting coupling interaction. Under the most favourable conditions, the superconducting transition temperature T_c ∼ ω_c, where ω_c is the Debye frequency related with local electron-phonon coupling. In general we have T¹ > T_c ⪢ T_c0 (T_c0 is the superconducting transition temperature of a usual superconductor). Therefore the system will firstly enter a coherent state before becoming a high-T_c superconductor.     

Theory of high-T c superconductivity based on the fermion-condensation quantum phase transition

A theory of high-temperature superconductivity based on the combination of the fermion-condensation quantum phase transition and the conventional theory of superconductivity is presented. This theory describes maximum values of the superconducting gap, which can be as big as Δ₁～0.1ε _F , with ε _F being the Fermi level. We show that the critical temperature 2T _c ?Δ₁. If the pseudogap exists above T _c , then 2T*?Δ₁ and T* is the temperature at which the pseudogap vanishes. A discontinuity in the specific heat at T _c is calculated. The transition from conventional superconductors to high-T _c ones as a function of the doping level is investigated. The single-particle excitations and their lineshape are also considered     

Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices

Since the discovery of high-temperature superconductivity in 1986 by Bednorz and Müller, great efforts have been devoted to finding out how and why it works. From the d-wave symmetry of the order parameter, the importance of antiferromagnetic fluctuations, and the presence of a mysterious pseudogap phase close to the Mott state, one can conclude that high-T_c superconductors are clearly distinguishable from the well-understood BCS superconductors. The d-wave superconducting state can be understood through a Gutzwiller-type projected BCS wavefunction. In this review article, we revisit the Hubbard model at half-filling and focus on the emergence of exotic superconductivity with d-wave symmetry in the vicinity of the Mott state, starting from ladder systems and then studying the dimensional crossovers to higher dimensions. This allows to confirm that short-range antiferromagnetic fluctuations can mediate superconductivity with d-wave symmetry. Ladders are also nice prototype systems allowing to demonstrate the truncation of the Fermi surface and the emergence of a Resonating Valence Bond (RVB) state with preformed pairs in the vicinity of the Mott state. In two dimensions, a similar scenario emerges from renormalization group arguments. We also discuss theoretical predictions for the d-wave superconducting phase as well as the pseudogap phase, and address the crossover to the overdoped regime. Finally, cold atomic systems with tunable parameters also provide a complementary insight into this outstanding problem.     

Ni2X2 (X = pnictide,chalcogenide, or B) based superconductors

We review the properties of Ni-based superconductors which contain Ni₂X₂ (X = As, P, Bi, Si, Ge, B) planes, a common structural element found also in the recently discovered FeAs superconductors. Strong evidence for the fully gapped nature of the superconducting state has come from field dependent thermal conductivity results on BaNi₂As₂. Coupled with the lack of magnetism, the majority of evidence suggests that the Ni-based compounds are conventional electron–phonon mediated superconductors. However, the increase in T_c in LaNiAsO with doping is anomalous, and mimics the behavior in LaFeAsO. Furthermore, comparisons of the properties of Ni- and Fe-based systems show many similarities, particularly with regards to structure–property relationships. This suggests a deeper connection between the physics of the FeAs superconductors and the related Ni-based systems which deserves further investigation.     

Mössbauer study of Tl containing highT c superconductors

Mössbauer spectroscopy, X-ray diffractometry, ESR and electrical resistivity measurements, were used to study highT _c (above 100 K) superconducting materials in order to get information about the effect of the preparation circumstances as well as about the anomalous behaviour in⁵⁷Fe and¹¹⁹Sn doped TlBaCaCu(⁵⁷Fe)O_4.5+δ and TlBaCuCu(¹¹⁹Sn)O_4.5+δ superconductors. We have found that the Mössbauer parameters strongly depend on the preparation circumstances. In many cases the presence of Mössbauer lines of nonsuperconducting oxide phases indicated that the iron and tin could not entirely built in into the lattice of superconductor. Four valence state tin and four valence state iron sites were identified in the superconducting phases. We have found anomalous temperature dependent changes in the⁵⁷Fe Mössbauer spectra of TlBaCaCu(⁵⁷Fe)O_4.5+δ samples around theT _c between 105–135 K. In this temperature range the total area of the spectrum temporary increases.     

Effect of impurity scattering on superconductivity in K2Cr3As3

Impurity scattering in a superconductor may serve as an important probe for the nature of superconducting pairing state. Here we report the impurity effect on superconducting transition temperature T c in the newly discovered Cr-based superconductor K₂Cr₃As₃.The resistivity measurements show that the crystals prepared using high-purity Cr metal（99.99%） have an electron mean free path much larger than the superconducting coherence length. For the crystals prepared using impure Cr that contains various nonmagnetic impurities, however, the T c decreases significantly, in accordance with the generalized Abrikosov-Gor’kov pair-breaking theory. This finding supports a non-s-wave superconductivity in K₂Cr₃As₃.     

Unconventional superconductivity

‘Conventional’ superconductivity, as used in this review, refers to electron–phonon-coupled superconducting electron pairs described by BCS theory. Unconventional superconductivity refers to superconductors where the Cooper pairs are not bound together by phonon exchange but instead by exchange of some other kind, e.g. spin fluctuations in a superconductor with magnetic order either coexistent or nearby in the phase diagram. Such unconventional superconductivity has been known experimentally since heavy fermion CeCu₂Si₂, with its strongly correlated 4f electrons, was discovered to superconduct below 0.6?K in 1979. Since the discovery of unconventional superconductivity in the layered cuprates in 1986, the study of these materials saw T_c jump to 164?K by 1994. Further progress in high-temperature superconductivity would be aided by understanding the cause of such unconventional pairing. This review compares the fundamental properties of 9 unconventional superconducting classes of materials – from 4f-electron heavy fermions to organic superconductors to classes where only three known members exist to the cuprates with over 200 examples – with the hope that common features will emerge to help theory explain (and predict!) these phenomena. In addition, three new emerging classes of superconductors (topological, interfacial – e.g. FeSe on SrTiO₃, and H₂S under high pressure) are briefly covered, even though their ‘conventionality’ is not yet fully determined.     

Suppression of superconductivity in YNi2B2C at the atomic disordering

The behavior of the electrical resistivity ρ(T), the superconducting transition temperature T _c , and the upper critical field H _c2(T) of a polycrystalline sample of YNi₂B₂C irradiated by thermal neutrons with the subsequent high-temperature isochronous annealing in the temperature interval T _ann = 100–1000°C has been studied. It has been found that the irradiation of YNi₂B₂C with a fluence of 10¹⁹cm^?2 leads to the suppression of the superconductivity. The final disordered state is reversible; i.e., the initial ρ(T), T _c , and H _c2(T) values are almost completely recovered upon annealing at up to T _ann = 1000°C. The quadratic dependence ρ(T) = ρ₀ + a ₂ T ² is observed for the sample in the superconducting state (T _c = 5.5?14.5 K). The coefficient a ₂ (proportional to the square of the electron mass m*) hardly changes. The form of the dependence of T _c on ρ₀ can be interpreted as the suppression of the two superconducting gaps, Δ₁ and Δ₂ (Δ₁ ～ 2Δ₂). The degradation rate of Δ₁ is about three times higher than that of Δ₂. The dependences dH _c2/dT on ρ₀ and T _c may be described by the relations for a superconductor in the intermediate limit (the coherence length ζ₀ is on the order of the electron mean free path l _tr) under the assumption of a nearly constant electron density of states on the Fermi level N(E _F). The observed behavior of T _c obviously does not agree with the widespread opinion about the purely electron-phonon mechanism of superconductivity in the compounds of this type supposing the anomalous type of superconducting pairing.     

Superconductivity in a simple model of the pseudogap state

An analysis is made of characteristics of the superconducting state (s-and d-pairing) using a simple, exactly solvable model of the pseudogap state produced by fluctuations of the short-range order (such as antiferromagnetic) based on a Fermi surface model with “hot” sections. It is shown that the superconducting gap averaged over these fluctuations is nonzero at temperatures higher than the mean-field superconducting transition temperature T _c over the entire sample. At temperatures T > T _c superconductivity evidently exists in isolated sections (“ drops”). Studies are made of the spectral density and the density of states in which superconducting characteristics exist in the range T > T _c however, in this sense the temperature T = T _c itself is no different in any way. These anomalies show qualitative agreement with various experiments using underdoped high-temperature superconducting cuprates.