Evidence for a striped phase of high T c superconductor at the Fermi surface

A complete Fermi surface in the normal state of superconducting Bi₂Sr₂CaCu₂O_8+δ at the optimum doping (T _c = 91K) has been measured by angle scanning photoemission spectroscopy using synchrotron radiation. The Fermi surface reveals broken segments and hot spots of high photointensity along lines of k _y = n:0:23Å^?1 in the (π; π) direction. The pseudogap observed at (π,0) in underdoped materials is one of this missing segments. The results indicate the presence of characteristic subbands of a superlattice of quantum stripes. This is formed by an ordered array of ～ 14Å large stripes.     

Modification of the superconducting order parameter Δ(k) by long-range interactions

It is demonstrated that the inclusion of long-range intersite interactions qualitatively modifies the dependence of a superconducting gap on quasimomentum for both s-and d-symmetry types. In particular, the order parameter of a superconducting phase with $d_{x^2 - y^2 } $ the symmetry type depends on two amplitudes and has the form Δ(k)=Δ₁(cosk _x ?cosk _y )+Δ₂(cos2k _x ?cos2k _y ). In this case, the theoretical dependence of the critical temperature on the degree of doping agrees with the experimental dependence.     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Superconducting coherent quasiparticle weight in high-Tc superconductor from angle-resolved photoemission

We study the doping and temperature dependence of the single-particle coherent weight, z_A, for high-T_c superconductors Bi₂Sr₂CaCu₂O_8+x using angle-resolved photoemission. We find that at low temperatures the coherent weight z_A at (π,0) is proportional to the carrier concentration x and that the temperature-dependence of z_A is similar to that of the c-axis superfluid density. We show that, for a wide range of carrier concentration, the superconducting transition temperature scales with the product of the low-temperature coherent weight and the maximum superconducting gap.     

Theory of high-T c superconductivity based on the fermion-condensation quantum phase transition

A theory of high-temperature superconductivity based on the combination of the fermion-condensation quantum phase transition and the conventional theory of superconductivity is presented. This theory describes maximum values of the superconducting gap, which can be as big as Δ₁～0.1ε _F , with ε _F being the Fermi level. We show that the critical temperature 2T _c ?Δ₁. If the pseudogap exists above T _c , then 2T*?Δ₁ and T* is the temperature at which the pseudogap vanishes. A discontinuity in the specific heat at T _c is calculated. The transition from conventional superconductors to high-T _c ones as a function of the doping level is investigated. The single-particle excitations and their lineshape are also considered     

High-resolution photoemission study of FeSr2YCu2O7+δ

We have performed high-resolution photoemission spectroscopy (PES) on FeSr₂YCu₂O_7+δ, of which superconductivity of T_c=49 K was recently reported. We clearly observed opening of a d-wave-like superconducting gap and estimated the maximum gap value (Δ_max) to be 10 meV at 15 K. This gap value gives 2Δ_max/k_BT_c∼5, suggesting a strong-coupling nature of superconductivity in FeSr₂YCu₂O_7+δ. Comparative PES study with superconducting and insulating samples shows that the valence band is rigidly shifted as a function of doping without evolution of additional states within the insulating gap.     

Temperature dependence of the energy gap in Bi2223 metal oxide superconductor

Spectroscopic studies of the silver-optimum-doped Bi2223 contacts show that the temperature dependence of the parameter Δ follows the BCS curve. However, the tunnel measurements performed for the same series of specimens did not reveal any temperature dependence of the energy gap Δ. The feature observed in the tunnel density of states was retained at temperatures T>T _c , manifesting the presence of the temperature-independent pseudogap E _p . The difference between the data obtained with tunnel spectroscopy and Andreev reflection spectroscopy is explained by the fact that the latter measures the true superconducting energy gap Δ_s(T), whereas the peaks of the tunneling conductivity are related to the total energy gap Δ of cuprates, which includes both the parameter Δ_s and the pseudogap $E_p :\Delta \approx \sqrt {\Delta _s^2 + E_p^2 } $ .     

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.     

Superconducting clusters in the pseudogap region

The upper boundary of the pseudogap state has been derived as a function of the doping within the impurity mechanism of high-T _c superconductivity under the assumption that, in the region bordering the superconducting phase on the side of the doping less than the optimum level (the pseudogap region), there exist finite superconducting clusters and the boundary of the superconducting phase corresponds to the threshold of the existence of an infinite superconducting cluster. The position of this boundary is in agreement with experiment. The condition imposed on the doping level at which the giant proximity effect should be observed has been derived. It means essentially that the thickness of the nonsuperconducting layer should be small compared to the average size of the superconducting clusters.     

Momentum dependence of pseudogap and superconducting gap in variation theory

To consider the origin of a pseudogap and a superconducting (SC) gap found in the high-T_c cuprates, we evaluated the momentum dependence of the singlet gap corresponding to the pseudogap and the SC gap in the t–J model, using an optimization variational Monte Carlo (VMC) method. In the underdoped regime, the singlet gap is significantly modified from the simple d_x²-y²(d)-wave gap (∝ cos k_x − cos k_y) by the contribution of long-range pairings. Its angular dependence at the quasi Fermi surface is qualitatively consistent with those experimentally observed in both hole and electron-doped cuprates. On the other hand, a SC gap is almost unchanged, preserving the original simple d-wave form. Thus, it seems that the incoherent part of the singlet gap mainly influences the forms of observed gaps.     

The influence of out-of-plane disorder on the formation of pseudogap and Fermi arc in Bi2Sr2−xRxCuOy (R=La and Eu)

We found that the length of the Fermi arc decreases with increasing out-of-plane disorder by performing angle resolved photoemission spectroscopy (ARPES) measurements in the superconducting state of optimally doped R=La and Eu samples of Bi₂Sr_2−xR_xCuO_y. Since out-of-plane disorder stabilizes the antinodal pseudogap as was shown in our previous study of the normal state, the present results indicate that this antinodal pseudogap persists into the superconducting state and decreases the Fermi arc length. We think that the shrinkage of the Fermi arc reduces the superfluid density, which explains the large suppression of the superconducting transition temperature when out-of-plane disorder is increased.     

Observation of two Andreev-like energy scales in La2-xSrxCuO4 superconductor-normal-metal-superconductor junctions

Conductance spectra measurements of highly transparent junctions made of superconducting La2-xSrxCuO4 electrodes and a nonsuperconducting La1.65Sr0.35CuO4 barrier are reported. At low temperatures below Tc, these junctions have two prominent Andreev-like conductance peaks with clear steps at energies Δ1 and Δ2 with Δ2>2Δ1. No such peaks appear above Tc. The doping dependence at 2 K shows that both Δ1 and Δ2 scale roughly as Tc. Δ1 is identified as the superconducting energy gap, while a few scenarios are proposed as for the origin of Δ2.     

ARPES studies of c-axis intracell coupling in Bi2Sr2CaCu2O8+δ

Using angle-resolved photoemission spectroscopy we have performed a detailed study of bilayer splitting in Bi₂Sr₂CaCu₂O_8+δ as a function of doping level and temperature. In heavily overdoped samples where the splitting is the clearest, we extract an intracell coupling t_⊥∼55 meV. As a function of photon energy the intensity ratio of the bonding and antibonding bands varies, allowing us to detect the bilayer splitting effect in the optimal and underdoped regimes. Surprisingly, with reduced doping the intracell coupling is not measurably reduced. Upon cooling to the superconducting state, a gap Δ opens in both bands yet the magnitude of the splitting remains unchanged.     

Non-Fermi-liquid behavior and d-wave superconductivity near the charge-density-wave quantum critical point

A scenario is presented, in which the presence of a quantum critical point due to formation of incommensurate charge density waves accounts for the basic features of the high temperature superconducting cuprates, both in the normal and in the superconducting states. Specifically, the singular interaction arising close to this charge-driven quantum critical point gives rise to the non-Fermi liquid behavior universally found at optimal doping. This interaction is also responsible for d-wave Cooper pair formation with a superconducting critical temperature strongly dependent on doping in the overdoped region and with a plateau in the optimally doped region. In the underdoped region a temperature dependent pairing potential favors local pair formation without superconducting coherence, with a peculiar temperature dependence of the pseudogap and a non-trivial relation between the pairing temperature and the gap itself. This last property is in good qualitative agreement with so far unexplained features of the experiments.     

Tunneling in single-layer Bi2Sr2CuO6+δ single crystals in high magnetic field

In tunneling experiments with high-quality single crystals of a single-layer cuprate superconductor Bi₂Sr₂CuO_6+δ using the break junction and point-contact techniques at T<T _c, the coexistence of the superconducting-state gap and the normal-state gap was observed. The values of the superconducting energy gap 2Δ_p?p are in the range from 13.4 to 15 meV (Δ_p?p=6.7–7.5 meV). The values of 2Δ_p?p are similar for two samples with T _c=4 K and for two samples with T _c=9–10 K and are independent of the carrier concentration. The normal-state gap, with the magnitude approximately equal to 50 meV, persists at T<T _c and in the magnetic field H?H _c2 up to 28 T. After the transition of the sample to the normal state, the intensity of the tunneling conductance rapidly decreases with increasing magnetic field strength and temperature. The observed large broadening of the tunneling spectra and large zero-bias conductances can be caused by a strong angular dependence of the superconducting gap. The tunneling results are in full agreement with the data of the angle-resolved photoemission spectroscopy measurements.     

Spin-orbit coupling in the superconducting phase and DDW states of high-T<Subscript>c</Subscript> cuprates

The effects of the spin-orbit coupling are considered for the high T _c cuprates with asymmetric superconducting gap (SC) and the d-density wave (DDW) phase due to its vital role in the experimental determination of the DDW state. Experiments predict an anisotropy in the DSC gap where |Δ(0,π)|>|Δ(π,0)| and the gap node deviates from the diagonal direction towards the k _x axis. Measurements also demonstrate DDW to be a possible candidate for the pseudogap in the underdoped phase. Due to the spin-orbit (SO) coupling in the low temperature orthorhombic (LTO) phase, the phase diagram of the cuprates suffers a change due to the modification of the T* value, the temperature characteristic of pseudogap, although T _c remains unaltered. Moreover, for a more generalized SO coupling, the DDW gap decreases with the angle but has no effect on the SC gap. We calculate the density of states in the various regimes of doping for the mixed SC+DDW states in the underdoped (UD) phase, SC state in the overdoped phase and also the DDW state in the UD phase and compare them with various theoretical and experimental works. The temperature dependence of the specific heat does not exhibit any qualitative change due to the SO coupling.     

Intrinsic tunneling study of underdoped Bi2Sr2-xLaxCuO6+δ superconductors

We report on a tunneling study of underdoped submicron Bi₂Sr_2-xLa_xCuO_6+δ (La-Bi2201) intrinsic Josephson junctions (IJJs), whose self-heating is sufficiently suppressed. The tunneling spectra are measured from 4.2 K up to the pseudogap opening temperature of T^* = 260 K. The gap value found from the spectral peak position is about 35 meV and has a weak temperature dependence both below and above the superconducting transition temperature of T_c = 29 K. Since the superconducting gap should have a value of 10-15 meV, our results indicate that the pseudogap (～35 meV) plays an important role in the underdoped La-Bi2201 intrinsic tunneling spectroscopy down to the lowest temperature of 4.2 K. However, the contribution of the superconducting gap can be separated by normalizing the spectra to the one near and above T_c, which shows that the IJJs can be a useful tool for the study of the electronic properties of the La-Bi2201 cuprate superconductors.     

Luminescence kinetics of dipolar excitons in circular traps

A detailed investigation of multiband superconductivity and Leggett’s mode in the Mg_1?x Al_xB₂ (0 ≤ x ≤ 0.45) system was carried out using tunneling and Andreev spectroscopy. Temperature dependences of superconducting gaps Δ_σ and Δ_π and their variation upon the degree of disorder and the Al concentration were studied. The dependence of the Leggett’s mode energy ε₀ upon the values of the gaps Δ_σ and Δ_π has been derived.     

Charge confinement effect in cuprate superconductors: an explanation for the normal-state resistivity and pseudogap

The fact that the stripe phase and pseudogap in the cuprate superconductors occur in the same doping regime is emphasized. A model based on charge confinement in self-organized nanometer-scale stripe fragments is proposed to understand various generic features of the normal-state energy gap including the magnitude of the gap, its anti-correlation with the superconducting gap, and the d-wave symmetry in its -dependence. This model also provides a basis for understanding other anomalous normal-state properties such as the linear temperature dependence of electrical resistivity. Received 7 December 1998