Admixture of an s-Wave Component to the d-Wave Gap Symmetry in High-Temperature Superconductors

Neutron crystal-field spectroscopy experiments in the Y- and La-type high-temperature superconductors HoBa₂Cu₃O_6.56, HoBa₂Cu₄O₈, and La_1.81Sr_0.15Ho_0.04- CuO₄ are reviewed. By this bulk-sensitive technique, information on the gap function is obtained from the relaxation behavior of crystal-field transitions associated with the Ho³⁺ ions which sit as local probes close to the superconducting copper-oxide planes. The relaxation data exhibit a peculiar change from a convex to a concave shape between the superconducting transition temperature T _c and the pseudogap temperature T ^* which can only be modeled satisfactorily if the gap function of predominantly d-wave symmetry includes an s-wave component of the order of 20–25%, independent of the doping level. Moreover, our results are compatible with an unusual temperature dependence of the gap function in the pseudogap region (T _c≤T≤T ^*), i.e., a break up of the Fermi surface into disconnected arcs.     

Anomalous raman scattering in the normal state of uederdoped crystals of YBA2Cu3O7-x

The integrated intensity of the electronic background between 200 and 700 cm^-1 observed in the Raman spectra of the YBa₂Cu₃O_7-x 1-2-3 system exciting at 1.16 eV shows three changes with temperature. This electronic background is due to the scattering between quasi-degenerate bands at the Fermi level with apical oxygen character which have neither CuO₂ nor chain character. One of these transitions coincides with the appearance of superconductivity in the system. This indicates that even if the opening of the gap in the apical oxygen electronic levels is not clearly observed, the interband transition between these two levels is coupled to the superconducting order parameter. The other two changes of the background intensity occur at temperatures greater thanT _c . The one at lower temperature is proportional toT _c and coincides probably with the appearance of self-organized electronic nanostructures already observed by EXAFS measurements in other HT_c material systems (La-Sr-Cu-O, Ba-Sr-Ca-Cu-O). The latter transition is observed at T_D>- T_c (where T_D decreases as T_c increases). This temperature coincides with the opening of a pseudogap that has been detected by several experimental techniques in underdoped High-T,. systems. The possibility to observe the opening of a pseudogap in the density of states by means of Raman scattering is analyzed in terms of different theoretical models that have been postulated to explain superconductivity in cuprates.     

Enhancing T c by Oxygen Isotope Substitution in Cuprates

The phase diagram of doped cuprates is generic. For low dopings a pseudogap is present at temperatures above the superconducting phase. The pseudogap phase is heterogeneous containing superconducting clusters which become phase coherent at T _c (Müller in J. Phys. Cond. Matter 19:251002, 2007). Most recent propositions suggest to increase the cluster size and therefore to enhance T _c . In the present note it is recalled that over a decade ago a giant oxygen isotope effect in low doped LSCO was reported. Thus, if indeed increasing the cluster sizes becomes possible, enhancing T _c towards the onset of the pseudogap phase, then it may be even further enhanced by ¹⁶O to ¹⁸O substitution.     

Pseudogap Analysis of Normal State Transport Behavior of 11 and 1111 Fe-Based Superconductors

In this paper we analyze transport data of different families of Fe-based superconductors, within a pseudogap framework. The Fe(Te, Se) samples exhibit s-shaped resistivity ρ(T) curves, while SmFeAs(O, F) ones present a departure from their high-temperature linear behavior. In either case, a characteristic temperature can be identified. These temperatures correspond to those at which abrupt changes in the temperature behavior of Hall resistance and of Seebeck coefficient occur, suggesting that they are signatures of pseudogaps opening in the density of states. The direct correlation between these characteristic temperatures and the superconducting transition temperatures suggests that the pseudogap and the superconducting state originate from the same mechanism. Scaling procedures of resistivity curves confirm such proportionality. On the other hand, excess Fe content in Fe(Te, Se) samples affects the pseudogap temperature much more strongly than the superconducting T _c . Finally, we find out that the pseudogap in the 1111 family is almost insensitive to disorder, as in high-T _c cuprates.     

The Pseudogap and the Superconducting Order Parameter in Inhomogeneous Bi2Sr2CaCu2O8+δ

Recent experiments on Bi₂Sr₂CaCu₂O₈₊ (Bi2212) have provided compelling evidence that the samples are inhomogeneous on a nanoscale, with spatially separated superconducting gap (SG) and nonsuperconducting, pseudogap (PG) regions that arise from hole–hole and particle–hole pairings, respectively. We compare and contrast the nonphase sensitive experiments that cannot distinguish these orderings from the phase-sensitive experiments that can. Although the wave vector dependence of the pseudogap is highly anisotropic, we conclude that in Bi2212, the c-axis quasiparticle tunneling is incoherent and that the c-axis supercurrent arises solely from a rather isotropic s-wave superconducting order parameter (OP) for T < T_c.     

Superconductivity in a Binary Boson-Fermion Mixture with Weak Interaction

A concept describing the origin of the pseudogap phase of high-T _c superconducting cuprates is discussed. Based on the idea about electron-composite boson mixture, existing below some value T _p in cuprates, first, an analytical expression for T _p is obtained. It is shown that T _p depends on interaction parameter responsible for two electron-composite boson transformation, as well on the boson formation energy. Second, the composite boson condensation temperature T _c, determined as a one below which the density of condensed bosons just ceases to be zero, is found. The reason why the behaviors of T _p and T _c in dependence on the interaction parameter may be so different is addressed.     

Physical Picture of High-T c Superconductivity in Cuprates

A simple physical picture of high-T _c superconductivity of CuO₂ planes is proposed. It possesses all characteristic features of HTS, such as a high superconducting transition temperature, the $d_{x^{2}-y^{2}}$ symmetry of order parameter, and the coexistence of a single-electron Fermi surface and a pseudogap in the normal state. Values of pseudogap are calculated for different doping levels.     

The Pseudogap and the Superconducting Order Parameter in Inhomogeneous Bi2Sr2CaCu2O8+δ

Recent experiments on Bi₂Sr₂CaCu₂O_8+δ (Bi2212) have provided compelling evidence that the samples are inhomogeneous on a nanoscale, with spatially separated superconducting gap (SG) and nonsuperconducting, pseudogap (PG) regions that arise from hole–hole and particle–hole pairings, respectively. We compare and contrast the nonphase sensitive experiments that cannot distinguish these orderings from the phase-sensitive experiments that can. Although the wave vector dependence of the pseudogap is highly anisotropic, we conclude that in Bi2212, the c-axis quasiparticle tunneling is incoherent and that the c-axis supercurrent arises solely from a rather isotropic s-wave superconducting order parameter (OP) for T < T_c.     

Fluctuations of the Order Parameter''s Phase in Layered Superconductors

The influence of the quantum fluctuations of the order parameter's phase on the critical temperature T _c is studied for a Josephson coupled layered superconductor. Two characteristic critical temperatures exist for a system, namely the superconducting critical temperature T ⁽²⁾ _c for a single layer estimated by the mean-field theory and the transition temperature for the outset or the superconducting phase coherence T* _c . The true critical temperature T _c is shown to vary inside the intervals T* _c T _c T ⁽²⁾ _c . For a strong quantum phase fluctuation limit, the superconducting layers become decoupled.     

The Transport Properties of Bi-Riched Bi2Sr2CuO6+δ Single Crystal

As-grown superconducting Bi-riched Bi₂Sr₂CuO₆₊ single crystals have been grown by the traveling solvent floating zone technique. The superconducting transition temperature T _c was about 6 K and the room temperature resistivity was about 2×10^–3 Ohm-cm. Transport properties, such as resistivity, magnetoresistance and Hall effect were measured from overdoped to underdoped samples annealed in inert atmosphere at 650°C. The transition temperature can be raised to 12 K after post annealing. The Hall measurement shows that the hole carrier density decrease after annealing. The temperature dependence of Hall angle is T ^1.5, not quadratic as observed for most high-T _c superconducting oxides such as YBa₂Cu₃O₇. The variation of onset T _c with different external magnetic field is very different from high-T _c superconductors. The in-plane conductivity shows the dependence of ln T and can be explained by weak localization theory.     

Spatially-Resolved NMR Study on Antiferromagnetic Vortex Core in HTSC

Magnetism in the vortex core of nearly-optimal doped Tl₂Ba₂CuO₆₊ (T _c=85 K) is investigated by a spatially-resolved NMR. The NMR relaxation rate T ^–1 ₁ at ²⁰⁵Tl site provides a direct evidence of the significant enhancement of the AF spin correlations in the vortex core region and shows clearly a local AF ordering of the core region Cu spins at T _N=20 K. Above T _N the core region is in the paramagnetic state which is a reminiscence of the state above the pseudogap temperature (T ^*–120 K), indicating that the pseudogap disappears within the vortex core.     

Physical properties of a new cuprate superconductor Pr2Ba4Cu7O15–δ

We present studies of the thermal, magnetic, and electrical transport properties of reduced polycrystalline Pr₂Ba₄Cu₇O_15?δ (Pr247) showing a superconducting transition at T_c=10–16 K, and compare them with those of as-sintered non-superconducting Pr247. The electrical resistivity in the normal state exhibited T² dependence up to approximately 150 K. A clear specific heat anomaly was observed at T_c for Pr247 reduced in a vacuum for 24 h, proving the bulk nature of the superconducting state. By the reduction treatment, the magnetic ordering temperature T_n of Pr moments decreased from 16 to 11 K, and the entropy associated with the ordering increased, while the effective paramagnetic moments obtained from the DC magnetic susceptibility varied from 2.72 to 3.13μ_B. The sign of Hall coefficient changed from positive to negative with decreasing temperature in the normal state of a superconducting Pr247, while that of the as-sintered one was positive down to 5 K. The electrical resistivity under high magnetic fields was found to exhibit T^α dependence (α=0.08–0.4) at low temperatures. A possibility of superconductivity in the so-called CuO double chains is discussed.

PACS: 74.72.Jt; 74.25.Bt; 75.40.Cx; 74.25.Fy     

Surface Superconducting State of Heavy-Fermion Superconductor CeIrIn5 Probed by CeIrIn5-Ag Junctions

The CeIrIn₅-Ag junctions of about 2×10^–9 cm^–2 area have been made using microfabrication techniques, and the surface superconducting state of CeIrIn₅, which has two characteristic temperatures T ₀ and T _c, has been investigated, where T ₀ and T _c are the transition temperature to zero-resistivity state and the bulk, thermodynamic transition temperature, respectively. The temperature, below which superconducting anomalies are observed, varies from junction to junction, and yet it is always well above T _c=0.4 K. This result, together with no indication of transition at T _c, suggests that at least the surface of CeIrIn₅ is in the superconducting state above T _c. The data on the critical current I _c in superconducting anomalies point to the possibility to define a local transition temperature for each junction.     

T c amplication and pseudogap at a shape resonance in a superlattice of quantum stripes

The shape resonance of the superconducting gap for a 2D electron gas in a superlattice of quantum stripes with a finite 1 D periodic potential barrier is studied when the Fermi level is tuned near the bottom of the third superlattice subband. The maximumT _c . appears at a critical charge densityT _c . Forp > p _c (in the underdoped regime) the chemical potential is tuned in a pseudogap region characterized by a decrease of the density of states and an opening of the partial gap at the Fermi surface. The pseudogap is closed forp< p _c (in the overdoped regime).     

On the Presence of 1D-Like Stripes in Superconducting Epitaxial La2-xSrxCuO4 thin Films

A large positive magnetoresistance (up to tens of percents) is observed in both underdoped (x < 0.15) and overdoped superconducting La_{2− x}Sr_xCuO₄ (LSCO) epitaxial thin films, at temperatures far above the superconducting critical temperature T _c . In the underdoped regime, this magnetoresistance cannot be described by the Kohler rule and is due to the influence of superconducting fluctuations. On the other hand, in the overdoped regime, the Kohler rule does not seem to be violated. The strong magnetoresistance above T _c can be related to the preformed superconducting pairs existing well above T _c but forming a phase coherent superconducting state below T _c . The observations support the idea of a close relation between the pseudogap and the superconducting gap and provide evidence for the presence of pre-pairs above T _c . Both the observed fluctuations and the observed magnetoresistance are in accordance with the existence of 1D-like stripes. These results are further supported by recent high magnetic field measurements (up to 55 T) of the transverse magnetoconductivity σ _xy, which goes to zero for T→0 K.     

On the Pseudogap State in Y- and La-Type High-Temperature Superconductors: Doping Dependence, Isotope Effects, and Electronic Properties Studied by Neutron Spectroscopy

The doping dependence as well as the oxygen and copper isotope effects on the pseudogap temperature T* were investigated by neutron spectroscopic experiments of the relaxation rate of crystal-field excitations in rare-earth based Y- and La-type high-temperature superconductors. We found three essential results from our truly bulk-sensitive experiments: (1) For all doping levels we had T* > T _c, even in the optimally doped and overdoped regimes. (2) In bilayer high-T _c compounds we observed huge oxygen and copper isotope effects on T*, which give evidence that the pseudogap formation is governed by lattice modes involving both the oxygen and copper ions. In single layer high-T _c compounds, on the other hand, no shift of T* was found for the copper isotope substitution. (3) Our results obtained for all doping levels support the unusual temperature dependence of the gap function in the pseudogap region reported for underdoped Bi-type compounds, i.e., a breakup of the Fermi surface into disconnected arcs in the temperature range T _c < T < T*.     

Superconductivity and Pseudogap States in λ-(BEDT-TSF)2GaCl4 : Microwave Conductivity Measurements

We have investigated the 45 GHz microwave response from an organic superconductor λ-(BEDT-TSF)₂GaCl₄ with T _c = 4.8 K. In the superconducting state, the London penetration depth saturates well below T _c , which may provide an evidence for a conventional s-wave paring. In the metallic state, σ₁ ^c deviates downward from σ _dc ^c , while σ₂ ^c , which should be zero in a conventional metallic state, increases exponentially toward T _c . This anomalous metallic state has been discussed in terms of a possible formation of incoherent electron pairs in so-called a pseudogap state.     

On the Possibility of s+d Wave Superconductivity Within a Two-Band Scenario for High Tc Cuprates

A variety of different experimental results show substantial evidence that the order parameter in high-temperature superconducting copper oxides is not of pure d-wave symmetry, but that an s-wave component exists, which especially shows up in experiments that test the c-axis properties. These findings are modeled theoretically within a two-band model with interband interactions, where the superconducting order parameters in the two bands are allowed to differ in symmetry. It is found that the coupling of order parameters with different symmetries (s+d) leads to substantial enhancements of the superconducting transition temperature T _c as compared to order parameters with only s-wave symmetry. An additional enhancement factor of T _c is obtained from the coupling of the bands to the lattice where moderate couplings favor superconductivity while too strong couplings lead to electron (hole) localization and consequently suppress superconductivity.     

Physical properties of a new cuprate superconductor Pr2Ba4Cu7O15−δ

We present studies of the thermal, magnetic, and electrical transport properties of reduced polycrystalline Pr₂Ba₄Cu₇O_15−δ (Pr247) showing a superconducting transition at T_c=10–16 K, and compare them with those of as-sintered non-superconducting Pr247. The electrical resistivity in the normal state exhibited T² dependence up to approximately 150 K. A clear specific heat anomaly was observed at T_c for Pr247 reduced in a vacuum for 24 h, proving the bulk nature of the superconducting state. By the reduction treatment, the magnetic ordering temperature T_N of Pr moments decreased from 16 to 11 K, and the entropy associated with the ordering increased, while the effective paramagnetic moments obtained from the DC magnetic susceptibility varied from 2.72 to 3.13μ_B. The sign of Hall coefficient changed from positive to negative with decreasing temperature in the normal state of a superconducting Pr247, while that of the as-sintered one was positive down to 5 K. The electrical resistivity under high magnetic fields was found to exhibit T^α dependence (α=0.08–0.4) at low temperatures. A possibility of superconductivity in the so-called CuO double chains is discussed.     

Low Temperature Scanning Tunneling Spectroscopy Studies of High Jc NdBa2Cu3O7 ? δ Single Crystals

We report low temperature scanning tunneling spectroscopy (STS) studies on NdBa₂Cu₃O_{7 –} (Nd123) single crystals. Two characteristic spectra with a nearly ohmic background spectrum and a V-shaped background are observed on the cleaved surfaces. The former spectum shows an inhomogeneous distribution of a superconducting energy gap (2) for STS differential conductance map. The latter shows a homogeneous distribution. It is probable that those differences are attributed to a tunneling current from different surface layers. The temperature dependence of tunneling conductance spectrum with a V-shaped background reveals that the superconducting gap disappears around T _c, and no pseudogap behavior exists above T _c.