Surface states and tunneling spectroscopy of high-Tcsuperconductors

Recent studies of high- T_csuperconductors have clarified new aspects of tunneling spectroscopy. The unconventional pairing states, i.e. d-wave symmetry in these materials have been established through various measurements. Differently from isotropic s-wave superconductors, d-wave pairing states have an internal phase of the pair potential. The internal phase modifies the surface states due to the interference effect of the quasiparticles. Along these lines, a novel formula of tunneling spectroscopy has been presented that fully takes into account of the anisotropy of the pair potential. The most essential difference of this formula from conventional ones is that it suggests the phase-sensitive capability of tunneling spectroscopy. The formula suggests that the symmetry of the pair potential is determined by the orientational dependence measurements of tunneling spectroscopy. Along these lines, several experiments have been performed on high-T_c superconductors. The observation of the zero-bias conductance peaks (ZBCP) on Y Ba₂Cu₃O_{7 − δ}strongly suggests the d_{x² − y²}-wave pairing states of hole-doped high-T_c superconductors. On the other hand, the absence of ZBCP on (electron-doped)Nd_1.85Ce_0.15CuO_{4 − δ}indicates that the pair potential of this material is a nodeless state. In this paper, recent developments of tunneling spectroscopy for anisotropic superconductors are reviewed both on theoretical and experimental aspects.     

Optical and Raman spectroscopy studies on Fe-based superconductors

A brief review of optical and Raman studies on the Fe-based superconductors is given, with special emphasis on the competing phenomenon in this system. Optical investigations on ReFeAsO (Re = rare-earth element) and AFe₂As₂ (A = alkaline-earth metal) families provide clear evidence for the gap formation in the broken symmetry states, including the partial gaps in the spin-density wave states of parent compounds, and the pairing gaps in the superconducting states for doped compounds. Especially, the superconducting gap has an s-wave pairing lineshape in hole-doped BaFe₂As₂. Optical phonons at zone center detected by Raman and infrared techniques are classified for several Fe-based compounds. Related issues, such as the electron–phonon coupling and the effect of spin-density wave and superconducting transitions on phonons, are also discussed. Meanwhile, open questions including the T-dependent mid-infrared peak at 0.6–0.7 eV, electronic correlation, and the similarities/differences between high-T_c cuprates and Fe-based superconductors are also briefly discussed. Important results from other experimental probes are compared with optical data to better understand the spin-density wave properties, the superconductivity, and the multi-band character in Fe-based compounds.     

Scanning tunneling microscopy and spectroscopy on iron-pnictides

Tremendous excitement has followed the recent discovery of superconductivity up to T_c = 56 K in iron–arsenic based materials (pnictides). This discovery breaks the monopoly on high-T_c superconductivity held by copper-oxides (cuprates) for over two decades and renews hope that high-T_c superconductivity may finally be theoretically understood and widely applied.Since scanning tunneling microscopy (STM) and spectroscopy (STS) have been key tools in the investigation and understanding of both conventional and unconventional superconductivity, these techniques are also applied to the pnictides. While the field is still in its early stages, several important achievements by STM and STS have been reported on the pnictides. In this paper, we will review their contribution towards an understanding of superconductivity in this new class of materials.     

Neutron scattering of iron-based superconductors

Low-energy spin excitations have been studied on polycrystalline LaFeAsO_1?xF_x samples by inelastic neutron scattering. The Q-integrated dynamical spin susceptibility χ″(ω) of the superconducting samples is found to be comparable to that of the magnetically ordered parent sample. On the other hand, χ″(ω) almost vanishes at x = 0.158, where the superconducting transition temperature T_c is suppressed to 7 K. In addition, χ″(ω) in optimally doped LaFeAsO_0.918F_0.082 with T_c = 29 K exhibits a spin resonance mode. The peak energy, E_res, when scaled by k_BT_c is similar to the value of about 4.7 reported in other high-T_c iron-based superconductors. This result suggests that there is intimate relationship between the dynamical spin susceptibility and high-T_c superconductivity in iron-based superconductors, and is consistent with a nesting condition between Fermi surfaces at the Γ and M points.     

Inelastic neutron scattering on iron-based superconductor BaFe2(As,P)2

Inelastic neutron scattering has been performed on powder sample of an iron-based superconductor BaFe₂(As_0.65P_0.35)₂ with superconducting transition temperature (T_c) = 30 K, whose superconducting (SC) order parameter is expected to have line node. In the normal state, constant-E scan of dynamical structure factor, S(Q, E), exhibits a peak structure centered at momentum transfer Q ～ 1.20 Å^?1, corresponding to antiferromagnetic wave vector. Below T_c, the redistribution of the magnetic spectral weight takes place, resulting in the formation of a peak at E ～ 12 meV and a gap below 6 meV. The enhanced magnetic peak structure is ascribed to the spin resonance mode, evidencing sign change in the SC order parameter similar to other iron-based high-T_c superconductors. It suggests that fully-gapped s_± symmetry dominates in this superconductor, which gives rise to high-T_c (=30 K) despite the nodal symmetry.     

Coexistence of magnetism and superconductivity in R1.4Ce0.6RuSr2Cu2O10 − δ(R = Eu,Sm and Gd)

The superconducting R_1.4Ce_0.6RuSr₂Cu₂O_10 − δ(R = Sm, Eu and Gd) withT_c ∼ 28, 32 and 42 K are also magnetically ordered atT_N ∼ 220, 122 and 180 K, respectively, thus,T_N ⪢ T_c. This is in contrast to intermetallic magnetic superconductors (such as RNi₂B₂C) in whichT_c ⪢  T_N. Magnetic susceptibility and Mossbauer spectroscopy show that superconductivity is confined to the CuO₂planes, whereas magnetism is due to the Ru sublattice. Irreversibility phenomena and magnetic anomalies, observed at low magnetic fields originate from antisymmetric exchange coupling of the Dzyaloshinsky–Moria type, and from spin reorientation of the Ru moments. The shielding fraction is about 100%, supporting the conclusion that the materials consist of a single phase, manifesting both magnetism and superconductivity at once.     

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.     

Novel superconducting characteristics and unusual normal-state properties in iron-based pnictide superconductors: 57FeNMR and 75AsNQR/NMR studies in REFeAsO1−y (RE = La,Pr, Nd) and Ba0.6K0.4Fe2As2

We discuss the novel superconducting characteristics and unusual normal-state properties of iron (Fe)-based pnictide superconductors REFeAsO_1?y (RE = La, Pr, Nd) and Ba_0.6K_0.4Fe₂As₂ (T_c = 38 K) by means of ⁵⁷FeNMR and ⁷⁵AsNQR/NMR. In the superconducting state of LaFeAsO_0.7 (T_c = 28 K), the spin component of the ⁵⁷Fe-Knight shift decreases to almost zero at low temperatures, which provide firm evidence of the superconducting state formed by spin-singlet Cooper pairing. The nuclear spin–lattice relaxation rates (1/T₁) in LaFeAsO_0.7 and Ba_0.6K_0.4Fe₂As₂ exhibit a T³-like dependence without a coherence peak just below T_c, indicating that an unconventional superconducting state is commonly realized in these Fe-based pnictide compounds. All these events below T_c are consistently argued in terms of an extended s_±-wave pairing with a sign reversal of the order parameter among Fermi surfaces. In the normal state, 1/T₁T decreases remarkably upon cooling for both the Fe and As sites of LaFeAsO_0.7. In contrast, it gradually increases upon cooling in Ba_0.6K_0.4Fe₂As₂. Despite the similarity between the superconducting properties of these compounds, a crucial difference was observed in their normal-state properties depending on whether electrons or holes are doped into the FeAs layers. These results may provide some hint to address a possible mechanism of Fe-based pnictide superconductors.     

Effect of the distortion of FeX4 (X = P,As) tetrahedron for the electronic structure of iron-pnictide system

We have performed an ab initio band structure calculation for the new high-T_c related iron-pnictide compounds LaFeXO (X = P, As), BaFe₂As₂, CaFe₂As₂ and LiFeAs (X = P, As). We found that LaFeXO and CaFe₂As₂ have many similarities in their band structures, which is expected by an ionic model. We found that the degree of distortion of FeAs₄ tetrahedra in LaFeAsO considerably changes the slope of the density of states near the Fermi level, and this result may explain why REFeAsO (RE = Nd, Sm, …) have higher T_c than LaFeAsO when electrons are doped. For all the above compounds, the density of states at the Fermi level decreases when X atoms approaches to the Fe–Fe plane, which means that the hybridization between Fe and X orbitals considerably expands the Fe d-bands.     

Smearing origin of zero-bias conductance peak in Ag-SiO-Bi2Sr2CaCu2O8+δ planar tunnel junctions: influence of diffusive normal metal verified with the circuit theory

We propose a new approach of smearing origins of a zero-bias conductance peak (ZBCP) in high-T_c superconductor tunnel junctions through the analysis based on the circuit theory for a d-wave pairing symmetry. The circuit theory has been recently developed from conventional superconductors to unconventional superconductors. The ZBCP frequently appears in line shapes for this theory, in which the total resistance was constructed by taking account of the effects between a d-wave superconductor and a diffusive normal metal (DN) at a junction interface, including the midgap Andreev resonant states (MARS), the coherent Andreev reflection (CAR) and the proximity effect. Therefore, we have analyzed experimental spectra with the ZBCP of Ag-SiO-Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) planar tunnel junctions for the {110}-oriented direction by using a simplified formula of the circuit theory for d-wave superconductors. The fitting results reveal that the spectral features of the ZBCP are well explained by the circuit theory not only excluding the Dynes's broadening factor but also considering only the MARS and the DN resistance. Thus, the ZBCP behaviors are understood to be consistent with those of recent studies on the circuit theory extended to the systems containing d-wave superconductor tunnel junctions.     

Transverse resistance of YBa2Cu3O7−δ single crystals

Measured is the transverse electrical resistance of YBa₂Cu₃O_7−δ single crystals with different oxygen deficiency values (δ) in the temperature range T_c − 300 K. The experimental data are approximated by an empiric expression accounting for the fluctuation conductivity near T_c and the semiconductor-like resistance regime. Our analysis of the concentration dependences of the fitting parameters, in particular, reveals that the resistance temperature dependence is largely affected by the sample's non-homogeneity. The latter, in turn, causes a T_c anisotropy and variable-range hopping conductivity between different phases. The deduced maximal values of the basal-plane coherence length, ξ_xy(0), are comparable with those for low-temperature superconductors.     

Point-contact Andreev-reflection spectroscopy in ReFeAsO1−xFx (Re = La,Sm): Possible evidence for two nodeless gaps

A deep understanding of the character of superconductivity in the recently discovered Fe-based oxypnictides ReFeAsO_1?xF_x (Re = rare-earth) necessarily requires the determination of the number of the gaps and their symmetry in k space, which are fundamental ingredients of any model for the pairing mechanism in these new superconductors. In the present paper, we show that point-contact Andreev-reflection spectroscopy experiments performed on LaFeAsO_1?xF_x (La-1111) polycrystals with T_c ～ 27 K and SmFeAsO_0.8F_0.2 (Sm-1111) polycrystals with T_c ～ 53 K gave differential conductance curves exhibiting two peaks at low bias and two additional structures (peaks or shoulders) at higher bias voltages, an experimental situation quite similar to that observed by the same technique in pure and doped MgB₂. The single-band Blonder–Tinkham–Klapwijk model is totally unable to properly fit the conductance curves, while the two-gap one accounts remarkably well for the shape of the whole experimental dI/dV vs. V curves. These results give direct evidence of two nodeless gaps in the superconducting state of ReFeAsO_1?xF_x (Re = La, Sm): a small gap, Δ₁, smaller than the BCS value (2Δ₁/k_BT_c ～ 2.2–3.2) and a much larger gap Δ₂ which gives a ratio 2Δ₂/k_BT_c ～ 6.5–9.0. In Sm-1111 both gaps close at the same temperature, very similar to the bulk T_c, and follow a BCS-like behaviour, while in La-1111 the situation is more complex, the temperature dependence of the gaps showing remarkable deviations from the BCS behaviour at T close to T_c.The normal-state conductance reproducibly shows an unusual, but different, shape in La-1111 and Sm-1111 with a depression or a hump at zero bias, respectively. These structures survive in the normal state up to T¹ ～ 140 K, close to the temperatures at which structural and magnetic transitions occur in the parent, undoped compound.     

Scanning tunneling spectroscopy on Bi2SrCaCuO6+δ

Scanning tunneling microscopy and scanning tunneling spectroscopy (STS) measurements were performed on Bi₂SrCaCuO₆ whose superconducting transition temperature T_c is about 80 K. The superconducting gap obtained by the STS measurements was found to be about 40 meV. This value is close to that of optimally doped Bi₂Sr₂CaCu₂O₈ which has similar T_c. The observed spatial inhomogeneity of the gap value was much smaller than that of Bi₂Sr₂CuO₆.     

Theoretical study of photoinduced superconductors in a two band model

A study of photoinduced high-T_c superconductivity is presented by canonical two-band BCS model containing Fermi surfaces of p and d holes. We have obtained two superconducting gaps from this model. Studies of chemical potential and hole concentration dependences on critical temperature (T_c) are made. The enhancement of T_c is found due to doping.The study of specific heat and density of states based on this model is also presented. The dependence T_c(n_h) for the system YBa₂Cu₃O_7?x (1 2 3) obtained theoretically agrees with the available experimental data.     

EPR observation of the spin pair correlation above Tc in lightly alkali metal-doped C60 fullerene

The existence of two temperatures: T_p-Cooper pairing and T_c-Bose–Einstein condensation in high temperature superconductors has been stipulated in a lightly potassium-doped C₆₀ by Magnetically Modulated Microwave Absorption. This doping level corresponds to the carrier density greater than the critical one: x>x₁. In case of rubidium lightly doped C₆₀, where the carrier density x was smaller than the critical one: x<x₁, anomalous EPR temperature dependence was observed. The characteristic temperature of bound electron pair formation T_p≈65 K and the energy gap 2Δ/k=30 K were estimated from the temperature dependence of the EPR signal intensity in non-superconducting state. These results suggest that the liquid fermions–liquid bosons transition can be observed as the opening of the spin gap at temperature T_p postulated in Micnas–Ranninger–Robaszkiewicz theory.     

Superconductivity in mesoscopic high-Tc superconducting particles

Based on the Hubbard model in the framework of non-phonon kinematical mechanism and taking into account the discreetness of an electronic energy spectrum, the superconducting critical temperature of a mesoscopic high-T_c sphere is analyzed as a function of doping and as a function of particle's radius. The critical temperature T_c is found to be an oscillating function of the radius of a particle. The size-dependent doping regime is revealed in high-T_c nanoparticles. Our analysis shows that each oscillation in T_c corresponds to the increase in a number of the energy levels in the sphere by 1. The amplitude of oscillations of T_c increases with decreasing R and can reach a value of 6 K for nanoparticles with sizes about 25 nm, in good agreement with experimental studies of YBa₂Cu₃O_7−δ nanoparticles.     

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.     

Zero bias conductance peak enhancement in Bi2Sr2CaCu2O8/Pb tunneling junctions

Recently, there has been tremendous interest on a tunneling feature called zero bias conductance peak (ZBCP) commonly found in high T_csuperconductor tunnel junctions. The interest stemmed from the feature’s root in the d-wave symmetry of high T_csuperconductors. In this paper we will review results of our study on ZBCP within a Pb/Bi₂Sr₂CaCu₂O₈(BSCCO) tunneling junction. This allows us to investigate the intricate interactions between s- and d-wave superconductivity. The ZBCP indeed demonstrates interesting properties when Pb becomes superconducting. We attribute these results to the suppression of the d-wave phase on the surface of BSCCO by the s-wave superconductivity from Pb through a proximity effect. We will also report some recent results on the magnetic field dependence of the ZBCP.     

Pairing modulations and phase separation instabilities in Bi2Sr2CaCu2O8 + δ

There is growing evidence that the unconventional spatial inhomogeneities in the doped high-_Tc$T_c$ superconductors are accompanied by the pairing of electrons, subsequent phase transitions and condensation into coherent states. We show that such pairing states can be obtained from phase separation instabilities near level crossings. Conditions for coherent pairing instabilities are examined using exact diagonalization of Hubbard-like pyramid structures under variation of coupling and interaction strengths. We also evaluate the behavior of the energy charge gap in the vicinity of level crossings using a parametrization of coupling to the apical site to represent out-of-plane effects. These results provide a simple microscopic explanation of (correlation induced) supermodulation of the coherent pairing gap observed in scanning tunneling microscopy measurements at atomic scale in Bi₂Sr₂CaCu₂O_8 + δ.     

Effects of Y2O3 additions on the oxygen diffusion in top-seeded melt growth processed YBa2Cu3O7−y superconductors

To understand the effect of Y₂BaCuO₅ (Y211)/YBa₂Cu₃O_7?y (Y123) interfaces on the oxygen diffusion in single grain YBa₂Cu₃O_7?y superconductors, single grain Y123 superconductors with 0.05 and 0.3 moles of Y₂O₃ additions were fabricated by a top-seeded melt growth (TSMG) process. Y123 compacts with Y₂O₃ additions were subjected to melt growth heating cycles with a cooling rate of 1 °C/h through a peritectic temperature (1015 °C) and then annealed at 450 °C for 200 h in flowing oxygen. The superconducting temperature (T_c) and critical current density (J_c) were estimated for the three different regions (top surface (s), intermediate (i) and center (c)) of samples. The amount of Y211/Y123 interface area in single grain Y123 superconductors was successfully controlled by Y₂O₃ additions. The T_c values of s regions were higher than those of i and c regions, which indicates the presence of more oxygen at the sample surfaces. In addition, the T_c values of i and c regions of the Y123 sample with 0.3 mole Y₂O₃ addition were higher than those of the same regions of the Y123 sample with 0.05 mole Y₂O₃ addition due to the promoted oxygen diffusion through Y211/Y123 interfaces and other related defects. In spite of the promoted oxygen diffusion by Y₂O₃ addition, the large T_c difference among the regions still existed, which suggests sluggish oxygen diffusion into single Y123 grains.