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 − δstrongly 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 − δindicates 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.     

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.     

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.     

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.     

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.     

Quasi-particle structure around a single vortex in high-Tc superconductors

For analyzing the checker-board like modulation of the local density of states (LDOS) around a vortex observed in the slightly overdoped Bi₂Sr₂CaCu₂O_x, we examined the effect of pseudogap state of high-T_c superconductors to the LDOS around the vortex. We first derived the Bogoliubov-de Gennes equation for d-wave superconductivity (d-SC) in the presence of d-spin density wave (d-SDW). Using the Fourier–Bessel expansion, we solved this equation for a single vortex state, numerically. We found that the peak of the bound states around E = 0 becomes small and modulation of the LDOS is observed for larger d-SDW order parameter.     

Preparation and characterization of Y1−xPrxBa2Cu3O7−δ single crystals

We present a reliable method for growing single crystals of Y_1−xPr_xBa₂Cu₃O_7−δ high-T_c superconductors in ZrO₂ crucibles. This method results in crystals with greatly improved superconducting properties compared to crystals grown with the previously reported methods which use Al₂O₃ crucibles. We describe techniques for crystal growth in both Al₂O₃ and ZrO₂ crucibles using an excess of BaCo₃ and CuO as the flux. The crystals were characterized by means of DC magnetic-susceptibility measurements, electrical-resistivity measurements, and electron microprobe analysis. The effects of Al contamination on the conditions for crystal growth and on the superconducting properties of the crystals are found to be quite significant.     

Scanning tunneling spectroscopy of a superlattice superconductor: Bi2Sr2CaCu2O8

It is clear that many of the cuprate superconductors are truly superlattices, composed of sheets whose individual superconducting critical temperatures may approach bulk values. Such a cuprate is Bi₂Sr₂CaCu₂O₈, often referred to as BSCCO-2212. Scanning tunneling spectroscopy (vacuum tunneling) applied toa-bBiO cleavage planes ofT_c≈90 K BSCCO single crystals under liquid helium simultaneously provides topography and local dI/dVspectra (superconducting density of states: DOS). The spectra, which are similar to those obtained from angle-resolved photoemission spectroscopy, confirm a large gap parameter Δ(x,y) on the uppermost layer. The dI/dVspectra do not unequivocally select order parameter symmetry, but are probably consistent with d-wave or anisotropic s-wave states. Spatial variations of Δ on a 100 Å scale are attributed to variation in BiO metallicity, originating in oxygen stoichiometry variations. A model is presented to explain the different dI/dVspectra which are seen, and associated with different local oxygen concentrations. This model, based on the superconducting proximity effect, assumes that in some regions the BiO uppermost layer is insulating and in other regions it is metallic, in the latter case induced superconductivity by proximity to the CuO₂planes. Our STM measurements appear to sample only the uppermost half cell of the crystal, and contain no obvious superlattice features. Recent measurements have confirmed Josephson radiation from voltage biasedc-axis pillars of BSCCO. From the point of view of the present work, the superconducting systems which weakly couple along thec-direction to create Josephson junctions are probably half-cell slabs of height 15.4 Å, each containing two CuO₂and two BiO layers, which act as single composite electrodes for the Josephson junctions.     

Pairing mechanisms and anisotropic superconductivity in layered crystals

A brief outline of the generalized BCS pairing theory is presented. The pairing of carriers can be due to the exchange of lattice-phonons or due to the exchange of electronic charge-density and spin-density excitations. It is argued that anisotropic physical properties in the normal as well as superconducting states in the new high-T_c materials are crucual in the development of any realistic theoretical approach, and in comparison of experimental results with correct BCS predictions involving superconductivity in layered crystals. The possibility of the break-down of the mean-field approximation is also discussed. As of now, the generalized BCS pairing approach is the only realistic microscopic theory available which may be applied to high-T_c superconductors.     

Magnetotransport and magnetotunneling in single-layer, two-layer, and three-layer Bi2Sr2Can−1CunOz (n=1,2,3) single crystals

In continuous magnetic fields H up to 28 T, we have studied the out-of-plane transport properties and tunneling characteristics of high-quality nondoped single crystals of the Bi-cuprate family: Bi₂Sr₂CuO_6+δ (Bi2201), Bi₂Sr₂CaCu₂O_8+δ (Bi2212) and Bi₂Sr₂Ca₂Cu₃O_10+δ (Bi2223) grown by an identical method. For all compounds the out-of-plane magnetotransport ρ_c(H) is negative in the temperature region where ρ_c(T) shows in the normal state a semiconducting-like temperature dependence. The negative magnetoresistance of ρ_c corresponds to the suppression of the semiconducting temperature dependence of ρ_c(T) which is found to be isotropic. For the Bi2201 compound, where the normal state can be reached in the available magnetic fields (28 T), a nearly complete suppression of the low-temperature upturn in ρ_c(T) is observed in the highest magnetic fields with a tendency towards a metallic behavior down to the lowest temperatures (0.4 K). Using the break-junction technique, especially for the Bi2212 and Bi2232 compounds, a clear superconducting gap structure can be observed. Both for temperatures above the critical temperature and for magnetic fields above the upper critical field, a pseudogap structure remains present in the tunneling spectra. The applied magnetic fields yield a stronger suppression of the superconducting state compared to that of the normal-state gap structures as manifested in ρ_c(T) transport and tunneling.     

Disordering effects in superconductors with anisotropic pairing: From Cooper pairs to compact bosons

In the weak-coupling BCS-theory approximation, normal impurities do not influence the superconducting transition temperature T _c in the case of isotropic s pairing. In the case of d pairing they result in a rapid destruction of the superconducting state. This is at variance with many experiments on the disordering of high-T _c superconductors, assuming that d pairing is realized in them. As the interelectronic attraction in a Cooper pair increases, the system transforms continuously from a BCS-type superconductor with “loose” pairs to a picture of superconductivity of “compact,” strongly coupled bosons. Near such a transition substantial deviations can be expected from the universal disorder dependence of T _c , as determined by the Abrikosov-Gor’kov equation, and T _c becomes more stable against disordering. Since high-T _c super-conducting systems fall into the transitional region from BCS-type pairs to compact bosons, these results can explain their relative stability against disordering. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 3, 258–262 (10 February 1997)     

Quasiparticle dissipation in the measurement process of phase qubit using high- superconductors

We discuss how to make use of high-T_c d-wave Josephson junctions in the construction of a phase qubit. We especially focus on the effect of the quasiparticle dissipation and the zero energy bound state on the macroscopic quantum tunneling which corresponds to the final measurement process of the d-wave phase qubit.     

Anatomy of Gossamer superconductivity

There are many systems in which two order parameters compete with each other. Of particular interest are systems in which these order parameters are both unconventional. In this contribution, we examine the representative example of a d-wave superconductor in the presence of a d-wave density wave, which has been suggested as a model for the pseudogap phase in the high-T_c superconductors. The physical properties of unconventional superconductivity in the presence of an anisotropic charge density wave are investigated within mean field theory. This model describes many features that were anticipated by an earlier phenomenological treatment of Tallon and Loram. In addition, the quasiparticle density of states in the presence of these two order parameters is calculated, which should be accessible by scanning tunneling microscopy.     

Influence of the charge concentration on the density of states in a two-dimensional superconducting system

The gap and the density of states of high-T_c superconductors have been a subject of paramount interest. In order to explain the observed experimental behavior several pairing mechanisms in high-temperature superconductivity have been considered, by theoretical calculations. In this work, within the BCS scheme, a two-band model with energy band overlapping is introduced. The gap parameter and the density of states in a two-dimensional superconducting system are studied as functions of the charge concentration. This model is applied to Bi2212 in order to obtain numerical results.     

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.     

Tunneling spectroscopy of layered superconductors: intercalated Li0.48(C4H8O)xHfNCl and De-intercalated HfNCl0.7

Tunneling measurements have been carried out on layered superconductors of the β(SmSI)-type – Li_0.48(THF)_xHfNCl (THF?=?C₄H₈O) and HfNCl_0.7 – by means of break-junction and scanning tunneling spectroscopy. Break-junction technique reveals Bardeen-Cooper-Schrieffer (BCS) – like gap structures with typical gap values of 2Δ (4.2 K) = 11–12 meV for Li_0.48(THF)_xHfNCl with the highest T_c = 25.5 K. Some of our measurements revealed multiple gaps and dip-hump structures, the largest gap 2Δ (4.2 K) ≈ 17–20 meV closing at T_c. This was shown both by break-junction and scanning-tunneling spectroscopy. From these experiments it stems that the highest obtained gap ratio 2Δ/k_BT_c ~ 8 substantially exceeds the BCS weak-coupling limiting values: ≈3.5 and ≈4.3 for s-wave and d-wave order parameter symmetry, respectively. Such large 2Δ/k_BT_c ratios are rather unusual for conventional superconductors but quite common to high-T_c cuprates, as well as to organic superconductors. Our studies allowed to collect much more evidence concerning the huge pairing energy in those materials and to investigate in detail the complexity of their superconducting gap spectra. An origin of the observed phenomena still remains to be clarified.     

Fourier Transform Spectroscopy of theYΣ–XΠiTransition of CuO

TheY²Σ⁺–X²Π_inear-infrared electronic transition of CuO was observed at high resolution for the first time. The spectrum was recorded with the Fourier transform spectrometer associated with the McMath–Pierce Solar Telescope at Kitt Peak. The excited CuO molecules were produced in a low pressure copper hollow cathode sputter with a slow flow of oxygen. Constants for theY²Σ⁺states of CuO are:T₀= 7715.47765(54) cm⁻¹,B= 0.4735780(28) cm⁻¹,D= 0.822(12) × 10⁻⁶cm⁻¹,H= 0.46(10) × 10⁻¹⁰cm⁻¹, γ = −0.089587(42) cm⁻¹, γ_D= 0.1272(79) × 10⁻⁶cm⁻¹,b_F= 0.12347(22) cm⁻¹, andc= 0.0550(74) cm⁻¹. ImprovedX²Π_iconstants are also presented.     

Critical temperature of layered highT c superconductors

We present and investigate a model for layered superconductors with single-electron interlayer tunneling and a unit cell containing an arbitrary number of sheets. For an effective pairing of two-dimensional origin,T _c is found to be independent of the layer spacings. However, pairing of three-dimensional nature, allowing for spacing dependent coupling strength, fits remarkably well the observed climb inT _c for the Bi–O and Tl–O layered systems, as the number of CuO₂ planes in the unit cell is increased from two to four and six. This agreement points to a weak coupling pairing mechanism of three-dimensional origin.     

Superexchange pairing and magnetic ordering in cuprate superconductors

The first analytic study of superexchange ion interaction in the cuprate layer of high-T _c superconductors is reported. It is shown that the superexchange nonadditive contributions are dominant in the onset of long-range magnetic order in a system, as well as are responsible for hole pairing to produce an energetically preferable, stable spin configuration. The Heisenberg parameter and the pair binding energy obtained ab initio are in a good quantitative agreement with experimental data. Fiz. Tverd. Tela (St. Petersburg) 41, 2127–2131 (December 1999)     

Measurement of the mass of the Λb baryon

In a data sample of four million hadronic Z decays collected with the ALEPH detector at LEP, four Λ_b baryon candidates are exclusively reconstructed in the Λ_b → Λ_c⁺π⁻ channel, with the Λ_c⁺ decaying into pK⁻π⁺, , or Λπ⁺π⁺π⁻. The probability of the observed signal to be due to a background fluctuation is estimated to be 4.2 × 10⁻⁴. The mass of the Λ_b is measured to be 5614±21 (stat.) ± 4 (syst.) MeV/c².