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.     

Interplay between unconventional superconductivity and heavy-fermion quantum criticality: CeCu2Si2 versus YbRh2Si2

In this paper the low-temperature properties of two isostructural canonical heavy-fermion compounds are contrasted with regards to the interplay between antiferromagnetic (AF) quantum criticality and superconductivity. For CeCu₂Si₂, fully-gapped d-wave superconductivity forms in the vicinity of an itinerant three-dimensional heavy-fermion spin-density-wave (SDW) quantum critical point (QCP). Inelastic neutron scattering results highlight that both quantum critical SDW fluctuations as well as Mott-type fluctuations of local magnetic moments contribute to the formation of Cooper pairs in CeCu₂Si₂. In YbRh₂Si₂, superconductivity appears to be suppressed at T???10?mK by AF order (T_N?=?70?mK). Ultra-low temperature measurements reveal a hybrid order between nuclear and 4f-electronic spins, which is dominated by the Yb-derived nuclear spins, to develop at T_A slightly above 2?mK. The hybrid order turns out to strongly compete with the primary 4f-electronic order and to push the material towards its QCP. Apparently, this paves the way for heavy-fermion superconductivity to form at T_c?=?2?mK. Like the pressure – induced QCP in CeRhIn₅, the magnetic field – induced one in YbRh₂Si₂ is of the local Kondo-destroying variety which corresponds to a Mott-type transition at zero temperature. Therefore, these materials form the link between the large family of about fifty low-T unconventional heavy – fermion superconductors and other families of unconventional superconductors with higher T_cs, notably the doped Mott insulators of the cuprates, organic charge-transfer salts and some of the Fe-based superconductors. Our study suggests that heavy-fermion superconductivity near an AF QCP is a robust phenomenon.     

Developments of the theory of spin fluctuations and spin fluctuation-induced superconductivity

Theory of spin fluctuations as developed in the past 30 years have played important roles in the theory of magnetism in metals, particularly in elucidating the properties around the magnetic instability or quantum critical points. Recently the theory has been extended to deal with the spin fluctuaion-mediated superconductivity with anisotropic order parameters in strongly correlated electron systems. These theoretical developments are briefly reviewed and the high temperature superconductivity of cuprates and organic and heavy electron superconductors are discussed in the light of these theories.     

Unconventional superconductivity pairing induced by antiferromagnetic spin fluctuations in layered organic superconductors

The unconventional character of the superconductivity in organic compounds κ-(ET)₂X is ascribed to an antiferromagnetic spin fluctuation induced pairing. Since the band structure involves two bands (±), we assume that the large amplitude spin fluctuations arise from the band with the best nesting properties (band +), while superconductivity pairing occurs in the other band (-).We show that the nesting properties may mimic either a chemical pressure (deuterization) or a hydrostatic one. Indeed, a change of the nesting ratio t₁/t₂, according to our model, induces a modification of the Fermi surface topology. The spin fluctuations strength in the system is affected and consequently the calculated effective coupling constant of superconductivity for the even-parity singlet pairing channel. Our theory appears to be qualitatively consistent with major experimental reports.     

The Nuclear Quadrupole Interaction in High Temperature Superconductors

Abstract

Since their discovery in 1986 [11], the high temperature superconducting (HTS) copper oxides have presented a continuing challenge to both experiment and theory. The identification of the underlying mechanism (or mechanisms) responsible for their superconductivity remains an unanswered question. Numerous theories have been proposed ranging from phonon-mediated pairing of the charge carriers, similar to the Bardeen–Cooper–Schrieffer (BCS) [2] theory developed for conventional low-temperature superconductors, to novel concepts independent of phonons [3–-l0]. For conventional superconductors the variation of the transition temperature T_c , with isotopic mass M (from BCS theory T_c ～ M^?a ) was an important verification of the contribution of electron-phonon interactions to electron pairing. Measurements of this effect of HTS cuprates resulted in isotope shifts much smaller than predicted by theory [ll-14], raising doubts about the role of phonons. However, Barbee [15] argued that the size of the isotope shift is not a unique indicator of phonon-mediated pairing. Since the HTS materials contain Cu ions with partially filled 3d shells, many of the alternative theories of HTS have focused on magnetic interactions and associated spin fluctuations [3–10]. The reader is referred to Ref. 16 for the details of other theories that have been proposed and to the article by Schrieffer and Anderson [17) for an overview discussion of the theory of high temperature superconductivity.     

HighT c superconductivity in the itinerant ising model: Spin singlet pairing

We study the spin singlet superconductivity exhibited in an itinerant Ising model Hamiltonian. This Hamiltonian models the Cu–O layers in highT _c oxide superconductors. Electrons are itinerant through nearest neighbor hopping. An Ising term is introduced to describe the antiferromagnetic superexchange interaction between electrons nominally on nearest neighbor Cu sites. We discuss various symmetry states allowed by the model, and give detailed predictions of the superconducting energy gap, specific heat, susceptibility, andT _c variation with carrier concentration. Results are compared to experimental data on highT _c superconductors and reasonable agreement is obtained.     

The CESR and spin wave studies of A-15 films in normal and superconducting states

The electron spin resonance studies have been reported for A-15 superconductors, namely Nb₃Ge, Nb₃Si and V₃Si possessing different T_c values and CESR, Platzmann-Wolff type spin waves, and spin waves of antiferromagnetic type are observed in all the samples. It is found that T_c of Nb₃Ge depends upon the presence and separation of spin wave absorptions from the CESR, and T_c is found to increase when the separation is reduced. It is concluded that the exchange interactions in the conduction band, as manifested by the behaviour of spin waves, are of antiferromagnetic type and they are responsible for superconductivity in A-15 materials studied.     

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.     

Theory of high-temperature superconductivity in cuprates

A microscopic theory of electronic spectrum and superconducting pairing in the high-temperature cuprate superconductors is presented. The theory is based on consideration of strong electron correlations within the Bogolyubov polar model. The Dyson equation is derived by using the equation of motion method for the thermodynamic Green functions in terms of the Hubbard operators. The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge fluctuations induced by kinematic interaction. The theory demonstrates that a strong Coulomb repulsion results in the anomalous electronic spectrum and unconventional (d-wave) superconducting pairing with high T _c mediated by the antiferromagnetic exchange and spin fluctuations.     

Theory and experimental evidence for superconductors with short coherence length

We sketch the theory of London superconductors with a complex order parameter undergoing a phase transition dominated by thermal fluctuations. This theory is essentially that of superfluid helium, appropriately modified. We derive relations between the transition temperatureT _c , the London penetration depth, the phase correlation length, the fall ofT _c with reduced thickness in thin slabs and the associated appearance of Kosterlitz-Thouless behavior. AtH _c2 thermal fluctuations drive the transition first order. Accordingly, magnetic properties will exhibit hysteresis phenomena and glassy behavior. Our analysis of recent specific heat and SR measurements and of experiments on ultrathin slabs as well as the experimental evidence for hysteresis phenomena and glassy behavior in magnetic properties reveal that this theory describes a large class of superconductors that encompasses the cuprates, bismuthates and fullerenes.     

Hole pairing induced by antiferromagnetic spin fluctuations

The effective interaction induced by antiferromagnetic spin fluctuations is considered in the random phase approximation in the context of the recently discovered highT _c oxide superconductors. This effective attraction favours a triplet pairing of holes. The implications of such pairing mechanism are discussed in connection with the current experimental observations.     

Electronic structure of high-T c superconductors and related compounds

We study a 5-band Hubbard model for the CuO₂ planes in cuprate super-conductors using Hartree-Fock mean-field theory including spiral spin density waves. For the half-filled case we recover a ZSA-like phase diagrambut with an additional new region characterized by strong covalency effects, which we call a covalent insulator region. We also provide a nonperturbative calculation ofJ _eff, the effective in-plane antiferromagnetic interaction, as a function of parameters of the model. We suggest that the high-T _c cuprates are in or very close to the covalent insulator region and within this we show that a consistent explanation of apparently conflicting high energy spectroscopic and magnetic measurements of the high-T _c cuprates can be given.     

Energy-scale phenomenology and pairing via resonant spin-charge motion in FeAs, CuO, heavy-fermion and other exotic superconductors

Muon spin relaxation (μSR) studies of the “1111” and “122” FeAs systems have detected static magnetism with variably sized ordered moments in their parent compounds. The phase diagrams of FeAs, CuO, organic BEDT, A₃C₆₀ and heavy-fermion systems indicate competition between static magnetism and superconductivity, associated with first-order phase transitions at quantum phase boundaries. In both FeAs and CuO systems, the superfluid density n_s/m^* at T→0 exhibits a nearly linear scaling with T_c. Analogous to the roton-minimum energy scaling with the lambda transition temperature in superfluid ⁴He, clear scaling with T_c was also found for the energy of the magnetic resonance mode in cuprates, (Ba,K)Fe₂As₂, CeCoIn₅ and CeCu₂Si₂, as well as the energy of the superconducting coherence peak observed by angle resolved photo emission (ARPES) in the cuprates near (π,0). Both the superfluid density and the energy of these pair-non-breaking soft-mode excitations determine the superconducting T_c via phase fluctuations of condensed bosons. Combining these observations and common dispersion relations of spin and charge collective excitations in the cuprates, we propose a resonant spin-charge motion/coupling, “traffic-light resonance,” expected when the charge energy scale ε_F becomes comparable to the spin fluctuation energy scale ?ω_SF~J, as the process which leads to pair formation in these correlated electron superconductors.     

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].     

A quantum of history

The critical temperature, T _c, for all presently known superconductors does not exceed 20°K. This fact obviously limits the range of applications of superconductivity in technology in a very fundamental way. On the whole, the reason why the value of T _c for ‘ordinary’ superconductors should not exceed 20–40 °K is fairly well understood on the basis of the existing theory of superconductivity. At the same time, there apparently could exist high temperature superconductors for which the temperature T _c would reach hundreds of degrees, or at least liquid air temperature. Possible means of producing high temperature superconductors are considered in this article. Special attention is paid to what can be called the exciton mechanism of superconductivity.     

The origin of the pseudogap phase: precursor superconductivity versus a competing energy gap scenario

In the last few years evidence has been accumulating that there are a multiplicity of energy scales which characterize superconductivity in the underdoped cuprates. In contrast to the situation in BCS superconductors, the phase coherence temperature T_c is different from the energy gap onset temperature T^∗. In addition, thermodynamic and tunneling spectroscopies have led to the inference that the order parameter Δ_sc is to be distinguished from the excitation gap Δ; in this way, pseudogap effects persist below T_c. It has been argued by many in the community that the presence of these distinct energy scales demonstrates that the pseudogap is unrelated to superconductivity. In this paper, we show that this inference is incorrect. We demonstrate that the difference between the order parameter and excitation gap and the contrasting dependences of T^∗ and T_c on hole concentration x and magnetic field H follow from a natural generalization of BCS theory. This simple generalized form is based on a BCS-like ground state, but with self-consistently determined chemical potential in the presence of arbitrary attractive coupling g. We have applied this mean field theory with some success to tunneling, transport, thermodynamics, and magnetic field effects. We contrast the present approach with the phase fluctuation scenario and discuss key features which might distinguish our precursor superconductivity picture from that involving a competing order parameter.     

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.     

EPR study of deoxygenated high-temperature superconductors

High-T _c superconductors are EPR silent but on a little deoxygenation of the high-T _c materials and their constituents, they yield rich but complex spectra. Spectra of (1) CuO, (2) BaCuO₂, (3) CaCuO₂, (4) Y₂Cu₂O₅, (5) La₂CuO₄, (6) La_2−x M _x CuO₄ (M=Sr, Ba), (7) Y based-123, (8) Bi based-2201, 2212, 2223, (9) Tl based-2223 and (10) Hg based-1212, 1223 have been studied. One thing common to all these materials is the CuO₂ plane which gets fragmented on deoxygenation and the inherent antiferromagnetic coupling is partially destroyed which results in the appearance of the spectra. The spectra recorded have been identified to be due to (1) Cu-monomer, (2) Cu-dimer, (3) Cu-tetramer, (4) Cu-octamer and (5) one signal at very low field which could not be identified because there was no structure in it and may be due to fragments higher than octamers. Very big fragments do not give any spectra because the original AF order probably remains intact in them. It is expected that when the fragments become magnetically isolated from the bulk, they produce EPR spectra. Most of the spectra have been analyzed and their spin-Hamiltonian parameters determined. The spectra of these species vary a little in terms of g-value and fine-structure splitting constant from sample to sample or even in the same sample and this may be attributed to some extra oxygen attachments retained with these species. Most frequently occurring species is the Cu-tetramer, (CuO)₄. As (CuO)₄ represents the unit cell of the all important two-dimensional CuO₂ plane of the high-T _c materials, its spectra have been argued to provide some clue to the mechanism of high-T _c superconductivity. The tetramer (CuO)₄ is a four one-half spin system and is essentially 16-fold degenerate by Heisenberg isotropic exchange, it is split into 6 components: one pentet, three triplets and two singlets. In superconductors the pentet appears to be the ground state and in the non-superconducting constituents the singlets seem to form the ground state as revealed by the temperature variation studies. In the case of La_1.854Sr_0.146CuO₄ we have found the signature of quantum stripe formation. The high-T _c superconductivity theories involving spin bag, antiferromagnetic spin fluctuations and magnons can be explained on the basis of Cu-tetramers.     

Possible mechanism for high-T c superconductivity

Based on recent experiments and numerical simulations on the glass behaviour of the new high-T _c superconductors, a microscopic mechanism is proposed. Disorder is found to play an important role. Pairing of holes and subsequent bose condensation on an antiferromagnetic background is proposed as a basic mechanism for high-T _c superconductivity.