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.     

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.     

自旋涨落与非常规超导配对

铜氧化物高温超导、铁基高温超导、重费米子超导和κ-型层状有机超导等超导体的超导态都与磁性有序态相邻,且超导能隙在动量空间一般存在变号.因此,这些超导体的超导机理被认为有别于常规BCS超导中的电子交换声子导致的各向同性s-波配对.在这些非常规超导中,自旋涨落被认为是导致电子形成库珀对的主要起源之一.本文主要以铜基和铁基高...     

高温超导体电子结构和超导机理的角分辨光电子能谱研究

超导是一种奇异的宏观量子现象.100多年来,已发现的超导体主要分为两类:以金属或者合金为代表的常规超导体以及以铜氧化物和铁基高温超导体为代表的非常规超导体.常规超导体的超导机理能被BCS超导理论完美解释,但高温超导体的超导机理至今仍未达成共识,已经成为凝聚态物理领域中长期争论且充满挑战的重大科学问题.从实验上揭示非常规超导材料的微观电子结构,是理解其奇异正常态和超导电性机理、建立新理论的前提和基础.角分辨光电子能谱技术,由于可以实现对材料中电子的能量、动量和自旋的直接测量,在高温超导研究中发挥了重要的作用.本文综述了我们利用角分辨光电子能谱技术在铜氧化物和铁基高温超导体电子结构和超导机理研究中取得的一些进展,主要包括母体的电子结构、正常态的非费米液体行为、超导态的能带和超导能隙结构以及多体相互作用等.这些结果为理解铜氧化物和铁基高温超导体的物性及超导机理提供了重要的信息.     

Inelastic neutron scattering studies of the spin and lattice dynamics in iron arsenide compounds

Although neutrons do not couple directly to the superconducting order parameter, they have nevertheless played an important role in advancing our understanding of the pairing mechanism and the symmetry of the superconducting energy gap in the iron arsenide compounds. Measurements of the spin and lattice dynamics have been performed on non-superconducting ‘parent’ compounds based on the LaFeAsO (‘1111’) and BaFe₂As₂ (‘122’) crystal structures, and on electron and hole-doped superconducting compounds, using both polycrystalline and single crystal samples. Neutron measurements of the phonon density-of-state, subsequently supported by single crystal inelastic X-ray scattering, are in good agreement with ab initio calculations, provided the magnetism of the iron atoms is taken into account. However, when combined with estimates of the electron–phonon coupling, the predicted superconducting transition temperatures are less than 1 K, making a conventional phononic mechanism for superconductivity highly unlikely. Measurements of the spin dynamics within the spin density wave phase of the parent compounds show evidence of strongly dispersive spin waves with exchange interactions consistent with the observed magnetic order and a large anisotropy gap. Antiferromagnetic fluctuations persist in the normal phase of the superconducting compounds, but they are more diffuse. Below T_c, there is evidence in three ‘122’ compounds that these fluctuations condense into a resonant spin excitation at the antiferromagnetic wavevector with an energy that scales with T_c. Such resonances have been observed in the high-T_c copper oxides and a number of heavy fermion superconductors, where they are considered to be evidence of d-wave symmetry. In the iron arsenides, they also provide evidence of unconventional superconductivity, but a comparison with ARPES and other measurements, which indicate that the gaps are isotropic, suggests that the symmetry is more likely to be extended-s_± wave in character.     

超导与自旋涨落

在常规超导体中,库珀对是由于电子与声子之间的相互作用而形成的.在此过程中,人们可以只考虑电子的电荷性质与声子之间的关联.然而在所谓的非常规超导体中,人们意识到一些其他类型的元激发也可能导致超导现象,而自旋涨落则可能是其中最重要的一种.在大多数非常规超导体中,都可以发现自旋涨落的身影.而在一些重要的体系中,包括铜基超导体、铁基超导体以及一些重费米子超导体体系等,可以确切地说,自旋涨落起到了关键的作用,尽管其相对应的超导机制仍然还不清楚.文章简单介绍了自旋涨落与超导电性之间的关联.     

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.     

Current issues in heavy fermion superconductivity

An attempt is made to summarize our current understanding of the superconductivity occuring in heavy fermion systems. The last three years have seen the discovery of two new superconductors (UNi₂Al₃ and UPd₂Al₃), much more use of directional probes to investigate the anisotropy of the gap structure, further experimental and theoretical inquiry into a possible coupling of magnetic and superconducting order parameters, wider application of pressure and uniaxial stress to examine the onset of ordering and some new indications of unconventional superconductivity. These topics will be reviewed along with others of current interest.     

BaCuS_2: A Superconductor with Moderate Electron-Electron Correlation

We show that the layered-structure BaCuS₂ is a moderately correlated electron system in which the electronic structure of the CuS layer bears a resemblance to those in both cuprates and iron-based superconductors.Theoretical calculations reveal that the in-plane d-p σ^*-bonding bands are isolated near the Fermi level.As the energy separation between the d and p orbitals are much smaller than those in cuprates and iron-based superconductors,BaCuS₂ is expected to be moderately correlated.We suggest that this material is an ideal system to study the competitive/collaborative nature between two distinct superconducting pairing mechanisms,namely the conventional BCS electron-phonon interaction and the electron-electron correlation,which may be helpful to establish the elusive mechanism of unconventional high-temperature superconductivity.     

High-pressure synthesis and physical properties of new iron (nickel)-based superconductors

We have utilized a high-pressure (HP) technique to synthesize a series of newly-discovered iron (nickel)-based superconductors. For the LnFeAsO-based superconductors (Ln = lanthanide), we show that the introduction of oxygen (O)-deficiency in the LnO layers, which is achievable only through HP process, is an effective way to dope electron carriers into the system, which results in yielding the superconducting transition temperature (T_c) comparable with those for F-substituted counterpart. The effect of O-deficiency, variation of Ln ions, and the external pressure on T_c are examined. All the experimental data indicate strong correlation between the crystal structure and the superconductivity of the oxypnictide superconductors. Upper critical field measurement on single crystalline sample of PrFeAsO_1?y shows the superconducting anisotropy of 5, which is smaller than cuprates. We also demonstrate that HP technique is applicable for the so-called ‘122’ systems, by showing the results on polycrystalline (Ca, Na)Fe₂As₂, (Ba, K)Fe₂As₂, as well as single crystal BaNi₂P₂ samples.     

Kinetic energy driven pairing in cuprate superconductors

Pairing occurs in conventional superconductors through a reduction of the electronic potential energy accompanied by an increase in kinetic energy. In the underdoped cuprates, optical experiments show that pairing is driven by a reduction of the electronic kinetic energy. Using the dynamical cluster approximation we study superconductivity in the two-dimensional Hubbard model. We find that pairing is indeed driven by the kinetic energy and that superconductivity evolves from an unconventional state with partial spin-charge separation, to a superconducting state with quasiparticle excitations.     

Breakdown of the Wiedemann-Franz law in strongly-coupled electron-phonon system,application to the cuprates

With the superconducting cuprates in mind, a set of unitary transformations was used to decouple electrons and phonons in the strong-coupling limit. While phonons remain almost unrenormalised, electrons are transformed into itinerent singlet and triplet bipolarons and thermally excited polarons. The triplet/singlet exchange energy and the binding energy of the bipolarons are thought to account for the spin and charge pseudogaps in the cuprates, respectively. We calculated the Hall Lorenz number of the system to show that the Wiedemann-Franz law breaks down due to the interference of the polaron and bipolaron contributions to heat flow. The model provides a quantitative fit to magnetotransport data in the cuprates. Furthermore we are able to extract the phonon component of the thermal conductivity with the use of experimental data and the model. Our results further validate the use of a charged Bose gas model to describe normal and superconducting properties of unconventional superconductors.Received: 9 February 2004, Published online: 23 July 2004PACS: 71.10.HF Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems - 71.27. + a Strongly correlated electron systems; heavy fermions - 71.38.Mx Bipolarons     

Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

In this short review, we first discuss the results, which are mainly devoted to the generalizations of the famous Kohn–Luttinger mechanism of superconductivity in purely repulsive fermion systems at low electron densities. In the context of repulsive-U Hubbard model and Shubin–Vonsovsky model we consider briefly the superconducting phase diagrams and the symmetries of the order parameter in novel strongly correlated electron systems including idealized monolayer and bilayer graphene. We stress that purely repulsive fermion systems are mainly the subject of unconventional low-temperature superconductivity. To get the high temperature superconductivity in cuprates (with T_C of the order of 100 K) we should proceed to the t–J model with the van der Waals interaction potential and the competition between short-range repulsion and long-range attraction. Finally we note that to describe superconductivity in metallic hydrogen alloys under pressure (with T_C of the order of 200 K) it is reasonable to reexamine more conventional mechanisms connected with electron–phonon interaction. These mechanisms arise in the attractive-U Hubbard model with static onsite or intersite attractive potential or in more realistic theories (which include retardation effects) such as Migdal–Eliashberg strong coupling theory or even Fermi–Bose mixture theory of Ranninger et al. and its generalizations.     

High magnetic field behavior of strongly correlated uranium-based compounds

Magnetic fields are now available to 100?T (pulsed), 45?T (static) at temperatures below 0.3?K. Such technical developments allow the study and tuning of (quantum) phase transitions, unusual magnetic structures and (high-temperature) superconductors in a variety of quantum materials. An especially important class of strongly correlated electron materials is the heavy Fermi liquids (HFLs) displaying numerous reduced-moment antiferromagnets, quantum critical points, unconventional superconductivity, hidden order (HO) and other mysterious ground states. Among the ‘heavy fermions’, the duality of 5f electrons in uranium-based compounds introduces interesting behavior that can be affected by large magnetic fields. I list a few such heavy fermion materials to be considered: URu₂Si₂ and its tunable hidden state, UBe₁₃ and UPt₃ as very HFL paramagnets that become superconducting, the magnetic superconductors UPd₂Al₃ and UNi₂Al₃, and the ferromagnetic s UGe₂, URhGe and UCoGe. There are also the suggested metamagnetic Fermi-surface reconstructed intermetallic compounds such as UPt₂Si₂ and UCo₂Si₂. Present research attention focuses on the high-field behavior (30–40?T) of URu₂Si₂ and its destruction of HO. These and other U-based systems, e.g. UAu₂Si₂, UIrGe, etc., expand the opportunities of high magnetic field studies far into the future.     

Spin fluctuations and high temperature superconductivity

Theory of spin fluctuations for itinerant magnetism and its application to high temperature superconductivity are reviewed. After a brief introduction to the whole subject the developments of the self-consistent renormalization theory of spin fluctuations are summarized with particular emphasis on critical properties at the quantum phase transitions. Most of the anomalous properties in the normal state of high-T_c cuprates are understood as due to the critical behaviours for the two dimensional antiferromagnetic metals. By analysing the nuclear magnetic relaxation rate and the T-linear term of resistivity, the set of parameters to specify the spin fluctuations are determined. It is shown that by using the parameters thus obtained one can describe other quantities as well, e.g. optical conductivity. Then we proceed to the theory of superconductivity by the spin fluctuation mechanism. After some discussion on the weak coupling treatments, the strong coupling theory is reviewed. It is shown that the set of parameters determined by the normal state properties of the high-T _c cuprates just give a transition temperature of the right order of magnitude. Among the parameters, the most sensitive one for T _c is the frequency spread of the spin fluctuations. This fact enables us to present a possible unified picture of the antiferromagnetic spin fluctuation-induced superconductors, including heavy fermion superconductors and organic superconductors. This point of view may be confirmed to a certain extent by microscopic calculations based on the fluctuation exchange approximation for the two-dimensional Hubbard models representing not only the cuprates but also organic and trellis lattice compounds. The review is concluded with some discussions on future problems, e.g. the pseudo spin-gap in the under-doped region.     

μSR studies of heavy fermion systems

We have performed both zero field and high transverse field measurements at dilution refrigerator temperatures on a number of heavy electron systems, examining the superconducting and magnetic properties of these interesting materials. Among the materials studied to date are UBe₁₃, URu₂Si₂ and U₆Fe. The magnetic field penetration depth in the superconducting state of UBe₁₃ is greater than 10000 Å, as no increase in the transverse field relaxation rate is observed belowT _c . A sharp increase in the precession frequency is seen, starting atT _c . This frequency shift shows little temperature dependence at low temperature; we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we have observed relaxation in high transverse field due to the formation of a flux lattice in U₆Fe, a material where the electron effective mass is rather lighter than in other heavy fermion systems. The relaxation exhibits a sharp onset atT _c=3.9 K, and is flat at low temperatures as expected for a conventional superconductor.     

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.     

Neutron studies of the iron-based family of high TC magnetic superconductors

We review neutron scattering investigations of the crystal structures, magnetic structures, and spin dynamics of the iron-based RFe(As, P)(O, F) (R = La, Ce, Pr, Nd), (Ba,Sr,Ca)Fe₂As₂, and Fe_1+x(Te–Se) systems. On cooling from room temperature all the undoped materials exhibit universal behavior, where a tetragonal-to-orthorhombic/monoclinic structural transition occurs, below which the systems become antiferromagnets. For the first two classes of materials the magnetic structure within the a–b plane consists of chains of parallel Fe spins that are coupled antiferromagnetically in the orthogonal direction, with an ordered moment typically less than one Bohr magneton. Hence these are itinerant electron magnets, with a spin structure that is consistent with Fermi-surface nesting and a very energetic spin wave bandwidth ～0.2 eV. With doping, the structural and magnetic transitions are suppressed in favor of superconductivity, with superconducting transition temperatures up to ≈55 K. Magnetic correlations are observed in the superconducting regime, with a magnetic resonance that follows the superconducting order parameter just like the cuprates. The rare earth moments order antiferromagnetically at low T like ‘conventional’ magnetic superconductors, while the Ce crystal field linewidths are affected when superconductivity sets in. The application of pressure in CaFe₂As₂ transforms the system from a magnetically ordered orthorhombic material to a ‘collapsed’ non-magnetic tetragonal system. Tetragonal Fe_1+xTe transforms to a low T monoclinic structure at small x that changes to orthorhombic at larger x, which is accompanied by a crossover from commensurate to incommensurate magnetic order. Se doping suppresses the magnetic order, while incommensurate magnetic correlations are observed in the superconducting regime.     

Structural classification and a binary structure model for superconductors

Based on structural and bonding features, a new classification scheme of superconductors is proposed to classify them into three classes: three-dimensional, two-dimensional and molecule-assembled superconductors. The sandwich model' for the high-T_c cuprates is extended to a `binary structure model': i.e., the crystal structure of most superconductors can be partitioned into two parts, a superconducting active component and a supplementary component. Partially metallic covalent bonding is found to be a common feature in all superconducting active components, and the electron states of the atoms in the active components usually make a dominant contribution to the energy band near the Fermi surface. Possible directions to explore new superconductors are discussed based on the structural classification and the binary structure model.     

Superconductivity and spin fluctuations

In the conventional superconductors, the Cooper pairs are mediated by phonons, which is a process where only the correlations between the phonons and the charge properties of the electrons are needed. However, superconductivity can also be derived from other types of elementary excitations. The spin fluctuations are arguably the most promising candidate that can mediate such unconventional superconductivity. In some of the important systems such as cuprates, Fe-based superconductors and heavy-fermion superconductors, spin fluctuations play a key role in the mechanism of their superconductivity although there are still many debates. In this paper, we will give a brief review on the correlation between the spin fluctuations and superconductivity.