Evidence for two energy scales in the superconducting state of optimally doped (Bi,Pb)2(Sr,La)2CuO6+delta

We use angle-resolved photoemission spectroscopy to investigate the energy gap(s) in (Bi,Pb)2(Sr,La)2CuO6+delta. We find that the spectral gap has two components in the superconducting state: a superconducting gap and pseudogap. Differences in their momentum and temperature dependence suggest that they represent two separate energy scales. Spectra near the node reveal a sharp peak with a small gap below T(c) that closes at T(c). Near the antinode, spectra are broad with a large energy gap of approximately 40 meV above and below T(c). The latter spectral shape and gap magnitude are almost constant across T(c), indicating that the pseudogap state coexists with the superconducting state below T(c), and it dominates spectra around the antinode. We speculate that the pseudogap state competes with the superconductivity by diminishing spectral weight in antinodal regions, where the superconducting gap is largest.     

Intrinsic tunneling spectra of Bi2(Sr(2-x)Lax)CuO(6+delta)

We have measured intrinsic-tunneling spectra of a single CuO-layer La-doped Bi2(Sr(2-x)Lax)CuO(6+delta) (Bi2201-Lax). Despite a difference of a factor of 3 in the optimal superconducting critical temperatures for Bi2201-La0.4 and Bi2212 (32 and 95 K, respectively) and different spectral energy scales, we find that the pseudogap vanishes at a similar characteristic temperature T* approximately 230-300 K for both compounds. We find also that, in Bi2201-Lax, pseudogap humps are seen as sharp peaks and, in fact, even dominate the intrinsic spectra.     

Absence of a loss of in-plane infrared spectral weight in the pseudogap regime of Bi(2)Sr(2)CaCu(2)O(8+delta)

The ab-plane reflectance of Bi(2)Sr(2)CaCu(2)O(8+delta) (Bi-2212) thin films was measured in the 30-25 000 cm(-1) range for one underdoped ( T(c) = 70 K), and one overdoped sample ( T(c) = 63 K) down to 10 K. We find similar behaviors in the temperature dependence of the normal-state infrared response of both samples. Above T(c), the effective spectral weight, obtained from the integrated conductivity, does not decrease when T decreases, so that no opening of an optical pseudogap is seen. We suggest that these are consequences of the pseudogap opening in the k = (0,pi) direction and of the in-plane infrared conductivity being mostly sensitive to the k = (pi,pi) direction.     

Discriminating the superconducting gap from the pseudogap in Bi(2)Sr(2)CaCu(2)O(8+delta) by interlayer tunneling spectroscopy

Tunneling spectroscopy using a very thin stack of intrinsic Josephson junctions has revealed that the superconducting gap is definitely different from the pseudogap in the Bi(2)Sr(2)CaCu(2)O(8+delta) system. In the underdoped region, the conductance peak arising from the superconducting gap is independently observed in the dI/dV-V curve and its position is much lower than that of the pseudogap. Near the optimum doping level and in the overdoped region, both peaks are located in close proximity. These findings are in conflict with a previous understanding of the pseudogap.     

Correlation of tunneling spectra in Bi(2)Sr(2)CaCu(2)O(8+delta) with the resonance spin excitation

New break-junction tunneling data are reported in Bi(2)Sr(2)CaCu(2)O(8+delta) over a wide range of hole concentration from underdoped (T(c) = 74 K) to optimal doped (T(c) = 95 K) to overdoped (T(c) = 48 K). The conductances exhibit sharp dips at a voltage, Omega/e, measured with respect to the superconducting gap. Clear trends are found such that the dip strength is maximum at optimal doping and that Omega scales as 4.9kT(c) over the entire doping range. These features link the dip to the resonance spin excitation and suggest quasiparticle interactions with this mode are important for superconductivity.     

Influence of disorder on the local density of states in high- T(c) superconducting thin films

Using a low temperature scanning tunneling microscope in the spectroscopic mode, we find that the disorder in a Bi(2)Sr(2)CaCu(2)O(8+delta) thin film modifies dramatically the quasiparticle local density of states. Small, but well-defined superconducting regions, coexisting with dominating semiconducting areas, show well-pronounced gap structures, similar to those observed previously in high-quality single crystals. Surprisingly, between these two regions, the detailed shape of the quasiparticle spectrum is virtually identical to the pseudogap previously observed at temperatures T>T(c), or in the vortex core, at 4.2 K. Thus, the role of the disorder in destroying the superconducting phase is comparable to that of the magnetic field or thermal fluctuations.     

Quasiparticle liquid in the highly overdoped Bi(2)Sr(2)CaCu(2)O(8+delta)

Results from the study of a highly overdoped (OD) Bi(2)Sr(2)CaCu(2)O(8+delta) with a T(c) = 51 K using angle-resolved photoemission spectroscopy are presented. We observe a sharp peak in the spectra near ( pi,0) that persists well above T(c), a nodal self-energy which approaches that seen for the Mo(110) surface state, and a more k-independent line shape at the Fermi surface than the lower-doped cuprates. This allows for a realistic comparison of the lifetime values to the experimental resistivity measurements. These observations point to the validity of the quasiparticle picture for the OD even in the normal state.     

Low energy excitation and scaling in Bi(2)Sr(2)Ca(n-1)Cu(n)O(2n+4) (n=1-3): angle-resolved photoemission spectroscopy

Angle-resolved photoemission spectroscopy (ARPES) has been performed on the single- to triple-layered Bi-family high-T (c) superconductors (Bi(2)Sr(2)Ca(n-1)Cu(n)O(2n+4), n=1-3). We found a sharp coherent peak as well as a pseudogap at the Fermi level in the triple-layered compound. Comparison among three compounds has revealed a universal rule that the characteristic energies of superconducting and pseudogap behaviors are scaled with the maximum T (c).     

Antiferromagnetic vortex core in Tl(2)Ba(2)CuO(6+delta) studied by nuclear magnetic resonance

Spatially resolved NMR is used to probe the magnetism in and around vortex cores of nearly optimally doped Tl(2)Ba(2)CuO(6+delta) (T(c)=85 K). The NMR relaxation rate T(-1)1 at the 205Tl site provides direct evidence that the antiferromagnetic (AF) spin correlation is significantly enhanced in the vortex core region. In the core region Cu spins show a local AF ordering with moments parallel to the layers 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(*) approximately 120 K), indicating that the pseudogap disappears within cores.     

Two- to three-dimensional crossover in the electronic structure of (Bi, Pb)2(Sr, La)2CuO(6+delta) from angle-resolved photoemission spectroscopy

The hole-concentration (x) dependence of the three-dimensional energy-momentum dispersion in (Bi, Pb)2(Sr, La)2CuO(6+delta) has been investigated by angle-resolved photoemission spectroscopy. For a heavily overdoped sample of T(c) < or = 0.5 K, an energy dispersion of approximately 10 meV in width is observed in the vicinity of the (pi, 0) point with varying momentum along the c axis (k(z)). This k(z) dispersion is zero for underdoped, optimally doped, and slightly overdoped samples up to a doping level corresponding to T(c) = 22 k. At higher doping levels we observe significant dispersion of the order of 10 meV (sample with T(c) < or = 0.5 K). This is clear evidence that at a doping value corresponding to T(c) = 22 K, a crossover from two- to three-dimensional electronic structure occurs.     

Electronic structure of the trilayer cuprate superconductor Bi(2)Sr(2)Ca(2)Cu(3)O(10+delta)

The low-energy electronic structure of the nearly optimally doped trilayer cuprate superconductor Bi(2)Sr(2)Ca(2)Cu(3)O(10+delta) is investigated by angle-resolved photoemission spectroscopy. The normal state quasiparticle dispersion and Fermi surface and the superconducting d-wave gap and coherence peak are observed and compared with those of single- and bilayer systems. We find that both the superconducting gap magnitude and the relative coherence-peak intensity scale linearly with T(c) for various optimally doped materials.     

Critical point and the nature of the pseudogap of single-layered copper-oxide Bi2Sr2-xLaxCuO6+delta superconductors

We apply strong magnetic fields of H=28.5 to 43 T to suppress superconductivity (SC) in the cuprates Bi2Sr2-xLaxCuO6+delta (x=0.65, 0.40, 0.25, 0.15, and 0), and investigate the low temperature (T) normal state by 63Cu nuclear spin-lattice relaxation rate (1/T1) measurements. We find that the pseudogap (PG) phase persists deep inside the overdoped region but terminates at x approximately 0.05, which corresponds to the hole doping concentration of approximately 0.21. Beyond this critical point, the normal state is a Fermi liquid that persists as the ground state when superconductivity is removed by the magnetic field. A comparison of the superconducting state with the H-induced normal state in the x=0.40 (Tc=32 K) sample indicates that there remains substantial part of the Fermi surface even in the fully developed PG state, which suggests that the PG and SC are coexisting matters.     

Quasiparticles in the superconducting state of Bi(2)Sr(2)CaCu(2)O(8+delta)

Recent improvements in momentum resolution lead to qualitatively new angle-resolved photoemission spectroscopy results on the spectra of Bi(2)Sr(2)CaCu(2)O(8+delta) (Bi2212) along the (pi,pi) direction, where there is a node in the superconducting gap. We now see the intrinsic line shape, which indicates the presence of true quasiparticles at all Fermi momenta in the superconducting state, and lack thereof in the normal state. The region of momentum space probed here is relevant for charge transport, motivating a comparison of our results to conductivity measurements by infrared reflectivity.     

Persistence of strong electron coupling to a narrow boson spectrum in overdoped Bi2Sr2CaCu2O(8+delta) tunneling data

A d-wave, Eliashberg analysis of break-junction and STM tunneling spectra on Bi2Sr2CaCu2O(8+delta) (Bi2212) reveals that the spectral dip feature is directly linked to strong electronic coupling to a narrow boson spectrum, evidenced by a large peak in alpha2F(omega). The tunneling dip feature remains robust in the overdoped regime of Bi2212 with bulk T(c) values of 56 K-62 K. This is contrary to recent optical conductivity measurements of the self-energy that suggest the narrow boson spectrum disappears in overdoped Bi2212 and therefore cannot be essential for the pairing mechanism. The discrepancy is resolved by considering the way each technique probes the electron self-energy, in particular, the unique sensitivity of tunneling to the off-diagonal or pairing part of the self-energy.     

Resonant spin excitation in an overdoped high temperature superconductor

An inelastic neutron scattering study of overdoped Bi(2)Sr(2)CaCu(2)O(8+delta) ( T(c) = 83 K) has revealed a resonant spin excitation in the superconducting state. The mode energy is E(res) = 38.0 meV, significantly lower than in optimally doped Bi(2)Sr(2)CaCu(2)O(8+delta) ( T(c) = 91 K, E(res) = 42.4 meV). This observation, which indicates a constant ratio E(res)/k(B)T(c) approximately 5.4, helps resolve a long-standing controversy about the origin of the resonant spin excitation in high temperature superconductors.     

Vortex fluctuations in underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) crystals

Vortex thermal fluctuations in heavily underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) (T(c)=69.4 K) are studied using Josephson plasma resonance. From the zero-field data, we obtain the c-axis penetration depth lambda(L,c)(0)=230+/-10 micrometer and the anisotropy ratio gamma(T). The low plasma frequency allows us to study phase correlations over the whole vortex solid state and to extract a wandering length r(w) of vortex pancakes. The temperature dependence of r(w) as well as its increase with dc magnetic field is explained by the renormalization of the vortex line tension by the fluctuations, suggesting that this softening is responsible for the dissociation of the vortices at the first order transition.     

High-field quasiparticle tunneling in Bi2Sr2CaCu2O(8+delta): negative magnetoresistance in the superconducting state

We report on the c-axis resistivity rho(c)(H) in Bi(2)Sr(2)CaCu(2)O(8+delta) that peaks in quasistatic magnetic fields up to 60 T. By suppressing the Josephson part of the two-channel (Cooper pair/quasiparticle) conductivity sigma(c)(H), we find that the negative slope of rho(c)(H) above the peak is due to quasiparticle tunneling conductivity sigma(q)(H) across the CuO2 layers below H(c2). At high fields (a) sigma(q)(H) grows linearly with H, and (b) rho(c)(T) tends to saturate ( sigma(c) not equal0) as T-->0, consistent with the scattering at the nodes of the d-wave gap. A superlinear sigma(q)(H) marks the normal state above T(c).     

Stepwise behavior of vortex-lattice melting transition in tilted magnetic fields in single crystals of Bi(2)Sr(2)CaCu(2)O(8 + delta)

The vortex-lattice melting transition in Bi(2)Sr(2)CaCu(2)O(8 + delta) single crystals was studied using in-plane resistivity measurements in magnetic fields tilted away from the c axis to the ab plane. In order to avoid the surface barrier effect which hinders the melting transition in the conventional transport measurements, we used the Corbino geometry of electric contacts. The complete H(c) - H(ab) phase diagram of the melting transition in Bi(2)Sr(2)CaCu(2)O(8 + delta) is obtained for the first time. The c-axis melting field component H(c)(melt) exhibits the novel, stepwise dependence on the in-plane magnetic fields H(ab) which is discussed on the basis of the crossing vortex-lattice structure. The peculiar resistance behavior observed near the ab plane suggests the change of phase transition character from first to second order.     

Novel anisotropy in the superconducting gap structure of Bi2Sr2CaCu2O(8+delta) probed by quasiparticle heat transport

Since the nature of pairing interactions is manifested in the superconducting gap symmetry, the exact gap structure, particularly any deviation from the simple d(x(2)-y(2)) symmetry, would help in elucidating the pairing mechanism in high- T(c) cuprates. Anisotropic heat transport measurement in Bi(2)Sr(2)CaCu(2)O(8+delta) reveals that the quasiparticle populations are different for the two nodal directions and thus the gap structure must be uniquely anisotropic, suggesting that pairing is governed by interactions with a rather complicated anisotropy. Intriguingly, it is found that the "plateau" in the magnetic-field dependence of the thermal conductivity is observed only in the b-axis transport.     

Nodal quasiparticle lifetime in the superconducting state of Bi(2)Sr(2)CaCu(2)O(8+delta)

We have measured the complex conductivity sigma of a Bi(2)Sr(2)CaCu(2)O(8+delta) thin film between 0.2 and 0.8 THz. We find sigma in the superconducting state to be well described as the sum of contributions from quasiparticles, condensate, and order parameter fluctuations which draw 30% of the spectral weight from the condensate. An analysis based on this decomposition yields a quasiparticle scattering rate on the order of k(B)T/Planck's over 2pi for temperatures below T(c).