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

Density of States and Spectral Function of a Superconductor out of a Quantum-Critical Metal

We analyze the validity of a quasiparticle description of a superconducting state above a metallic quantum-critical point (QCP). A normal state at a QCP is a non-Fermi liquid with no coherent quasiparticles. A superconducting order gaps out low-energy excitations, except for a sliver of states for non-s-wave gap symmetry, and at a first glance, restores coherent quasiparticle behavior. We argue that this does not necessarily hold as the fermionic self-energy may remain singular above the gap edge. This singularity gives rise to markedly non-BCS behavior of the density of states and to the appearance of a nondispersing mode at the gap edge in the spectral function. We analyze the set of quantum-critical models with an effective dynamical four-fermion interaction V(Ω)∝1/Ω^{γ}, where Ω is a frequency of a boson, which mediates the interaction. We show that coherent quasiparticle behavior in a superconducting state holds for γ<1/2, but breaks down for larger γ. We discuss signatures of quasiparticle breakdown and compare our results with the photoemission data for Bi2201 and Bi2212.

Quasiparticle Scattering in a Superconductor near a Nematic Critical Point: Resonance Mode and Multiple Attractive Channels

We analyze the scattering rate for 2D fermions interacting via soft nematic fluctuations. The ground state is an s-wave superconductor, but other pairing channels are almost equally attractive. This strongly alters the scattering rate: At energies beyond the pairing gap Δ, it is renormalized by contributions from all pairing channels. At energies of order Δ, it is determined by the competition between scattering into a gapped continuum and dispersing nematic resonance. The outcome is a "peak-peak-dip-hump" spectrum, similar, but not identical, to the "peak-dip-hump" structure in the cuprates.

Momentum-resolved evolution of the Kondo lattice into "hidden order" in URu2Si2

We study, using high-resolution angle-resolved photoemission spectroscopy, the evolution of the electronic structure in URu2Si2 at the Γ, Z, and X high-symmetry points from the high-temperature Kondo-screened regime to the low-temperature hidden-order (HO) state. At all temperatures and symmetry points, we find structures resulting from the interaction between heavy and light bands related to the Kondo-lattice formation. At the X point, we directly measure a hybridization gap of 11 meV already open at temperatures above the ordered phase. Strikingly, we find that while the HO induces pronounced changes at Γ and Z, the hybridization gap at X does not change, indicating that the hidden-order parameter is anisotropic. Furthermore, at the Γ and Z points, we observe the opening of a gap in momentum in the HO state, and show that the associated electronic structure results from the hybridization of a light electron band with the Kondo-lattice bands characterizing the paramagnetic state.

The electronic structure of the high-TC cuprates within the hidden rotating order

The doping dependence of the Fermi surface and energy distribution curves of the high-T(C) cuprate materials La(2 - x)Sr(x)CuO(4) and Bi(2)Sr(2)CaCu(2)O(8 + δ) are analyzed within the rotating antiferromagnetism theory. Using three different quantities; the k-dependent occupation probability, the spectral function, and the chemical potential (energy spectra), the Fermi surface is calculated and compared to experimental data for La(2 - x)Sr(x)CuO(4). The Fermi surface we calculate evolves from hole-like pockets in the underdoped regime to large electron-like contours in the overdoped regime. This is in agreement with recent findings by Sebastian et al for the α-pocket of Y Ba(2)Cu(3)O(6 + x) (2010 Phys. Rev. B 81 214524). In addition, the full width at half maximum of the energy distribution curves is found to behave linearly with their peak position in agreement with experiment for Bi(2)Sr(2)CaCu(2)O(8 + δ). The effect of scattering on both the Fermi surface and energy distribution curves is examined.

Anomalous momentum dependence of the superconducting coherence peak and its relation to the pseudogap of La1.85Sr0.15CuO4

We performed high-resolution angle-resolved photoemission spectroscopy on La1.85Sr0.15CuO4 to study the nature of the single-particle excitation gap. We found that there is a well-defined superconducting coherence peak in the off-nodal region while it is strongly suppressed around the antinode. The momentum dependence of the single-particle excitation gap shows a striking deviation from the dx-y2--wave symmetry with anomalous enhancement around the antinode in both the superconducting and the pseudogap state. The observed close correlation between the superconducting coherence peak and the pseudogap suggests a substantial contribution of the pseudogap to the anomalous behavior of the gap in the superconducting state.

Dual character of the electronic structure of YBa2Cu4O8: the conduction bands of CuO2 planes and CuO chains

We use microprobe angle-resolved photoemission spectroscopy (microARPES) to separately investigate the electronic properties of CuO2 planes and CuO chains in the high temperature superconductor, YBa2Cu4O8. For the CuO2 planes, a two-dimensional (2D) electronic structure is observed and, in contrast to Bi2Sr2CaCu2O8+delta, the bilayer splitting is almost isotropic and 50% larger, which strongly suggests that bilayer splitting has no direct effect on the superconducting properties. In addition, the scattering rate for the bonding band is about 1.5 times stronger than the antibonding band and is independent of momentum. For the CuO chains, the electronic structure is quasi-one-dimensional and consists of a conduction and insulating band. Finally, we find that the conduction electrons are well confined within the planes and chains with a nontrivial hybridization.

Anomalous quasiparticle lifetime and strong electron-phonon coupling in graphite

We have performed ultrahigh-resolution angle-resolved photoemission spectroscopy on high-quality single crystals of graphite to elucidate the character of low-energy excitations. We found evidence for a well-defined quasiparticle (QP) peak in the close vicinity of the Fermi level comparable to the nodal QP in high-T(c) cuprates, together with the mass renormalization of the band at an extremely narrow momentum region around the K(H) point. Analysis of the QP lifetime demonstrates the presence of strong electron-phonon coupling and linear energy dependence of the QP scattering rate indicative of a marked deviation from the conventional Fermi-liquid theory.

High-transition-temperature superconductivity in the absence of the magnetic-resonance mode

The fundamental mechanism that gives rise to high-transition-temperature (high-T(c)) superconductivity in the copper oxide materials has been debated since the discovery of the phenomenon. Recent work has focused on a sharp 'kink' in the kinetic energy spectra of the electrons as a possible signature of the force that creates the superconducting state. The kink has been related to a magnetic resonance and also to phonons. Here we report that infrared spectra of Bi2Sr2CaCu2O8+delta (Bi-2212), shows that this sharp feature can be separated from a broad background and, interestingly, weakens with doping before disappearing completely at a critical doping level of 0.23 holes per copper atom. Superconductivity is still strong in terms of the transition temperature at this doping (T(c) approximately 55 K), so our results rule out both the magnetic resonance peak and phonons as the principal cause of high-T(c) superconductivity. The broad background, on the other hand, is a universal property of the copper-oxygen plane and provides a good candidate signature of the 'glue' that binds the electrons.

Oxygen isotope effect in the ab-plane reflectance of underdoped YBa(2)Cu(3)O(7-delta)

We have measured the effect of oxygen isotope substitution on the ab-plane reflectance of underdoped YBa(2)Cu(3)O(7-delta). The frequency shift of the transverse optic phonons due to the substitution of 16O by 18O yields an isotope effect of the expected magnitude for copper-oxygen stretching modes with alpha=0.5+/-0.1. The reflectance shoulder at 400-500 cm(-1) shows a much smaller exponent of alpha=0.1+/-0.1 in the normal state and alpha=0.23+/-0.1 in the superconducting state. These observations suggest that the shoulder is of electronic origin and not due to a phonon mode as has been suggested recently.

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).

Spectral measurement of the Hall angle response in normal state cuprate superconductors

We measure the temperature and frequency dependence of the complex Hall angle for normal state YBa(2)Cu(3)O(7) films from dc to far-infrared frequencies (20-250 cm(-1)) using a new modulated polarization technique. We determine that the functional dependence of the Hall angle on scattering does not fit the expected Lorentzian response. We find spectral evidence supporting models of the Hall effect where the scattering Gamma(H) is linear in T, suggesting that a single relaxation rate, linear in temperature, governs transport in the cuprates.

Interaction-induced collapse of a section of the Fermi sea in the zigzag Hubbard ladder

Using the next-nearest-neighbor (zigzag) Hubbard chain as a one-dimensional model, we investigate the influence of interactions on the position of the Fermi wave vectors with the density-matrix renormalization-group technique. For suitable choices of the hopping parameters we observe that electron-electron correlations induce very different renormalizations for the two different Fermi wave vectors, which ultimately lead to a complete destruction of one section of the Fermi sea in a quantum critical point.

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.

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.

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.

Coherent quasiparticle weight and its connection to high-T(c) superconductivity from angle-resolved photoemission

We study the doping and temperature dependence of the single-particle coherent weight, z(A), for high- T(c) superconductors Bi(2)Sr(2)CaCu(2)O(8+x) using angle-resolved photoemission. We find that at low temperatures the coherent weight z(A) at (pi,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.

Projected wave functions and high temperature superconductivity

We study the Hubbard model with parameters relevant to cuprates using variational Monte Carlo for projected d-wave states. For doping 0<x approximately less than or equal to 0.35 we obtain a superconductor whose order parameter Phi(x) tracks the observed nonmonotonic T(c)(x). The variational parameter Delta(var)(x) scales with the (pi,0) "hump" and T* seen in photoemission. Projection leads to incoherence in the spectral function and from the singular behavior of its moments we obtain the nodal quasiparticle weight Z approximately x though the Fermi velocity remains finite as x-->0. The Drude weight D(low) and superfluid density are consistent with experiment and D(low) approximately Z.

Strong spin-fluctuation effects on the photoemission line shape in the normal state of high-T(c) cuprates

We have studied the quasiboson model for photoemission from cuprates in the normal state, where quasiparticles are coupled to collective spin excitations strongly enhanced near momentum (pi,pi). The present model has a benefit to describe the observed crossover from the overdoped to the underdoped cases because it is in principle an infinite-order theory in the limit of narrow bandwidth. The anomalous dependences of the photoemission line shape on the momentum and hole concentration are consistently understood within the model with no adjustable parameter except for a doping-independent coupling constant.

Microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x

The parent compounds of the copper oxide high-transition-temperature (high-Tc) superconductors are unusual insulators (so-called Mott insulators). Superconductivity arises when they are 'doped' away from stoichiometry. For the compound Bi2Sr2CaCu2O8+x, doping is achieved by adding extra oxygen atoms, which introduce positive charge carriers ('holes') into the CuO2 planes where the superconductivity is believed to originate. Aside from providing the charge carriers, the role of the oxygen dopants is not well understood, nor is it clear how the charge carriers are distributed on the planes. Many models of high-Tc superconductivity accordingly assume that the introduced carriers are distributed uniformly, leading to an electronically homogeneous system as in ordinary metals. Here we report the presence of an electronic inhomogeneity in Bi2Sr2CaCu2O8+x, on the basis of observations using scanning tunnelling microscopy and spectroscopy. The inhomogeneity is manifested as spatial variations in both the local density of states spectrum and the superconducting energy gap. These variations are correlated spatially and vary on the surprisingly short length scale of approximately 14 A. Our analysis suggests that this inhomogeneity is a consequence of proximity to a Mott insulator resulting in poor screening of the charge potentials associated with the oxygen ions left in the BiO plane after doping, and is indicative of the local nature of the superconducting state.

Superfluid density in the d-density-wave scenario

Recently Chakravarty, Laughlin, Morr, and Nayak [Phys. Rev. B 62, 4880 (2000)] made an interesting proposal that the cuprate superconductors possess a hidden " d-density-wave" (DDW) order. We study the implication of this proposal for the superfluid density rho(s). We find that it predicts a temperature gradient [d rho(s)/dT](T = 0) that is strongly doping dependent near the critical doping at which the superconducting gap vanishes. This demonstrates that the DDW scenario is inconsistent with existing well-established experimental data.

High-resolution photoemission study of MgB2

We have performed high-resolution photoemission spectroscopy on MgB2 and observed opening of a superconducting gap with a narrow coherent peak. We found that the superconducting gap is s like with the gap value ( Delta) of 4.5+/-0.3 meV at 15 K. The temperature dependence (15-40 K) of the gap value follows well the BCS form, suggesting that 2Delta/k(B)T(c) at T = 0 is about 3. No pseudogap behavior is observed in the normal state. The present results strongly suggest that MgB2 is categorized into a phonon-mediated BCS superconductor in the weak-coupling regime.

Incipient nodal pairing in planar d-wave superconductors

The possibility of a second pairing transition d --> d + is ( d + id') in planar d-wave superconductors which occurs in the absence of external magnetic field, magnetic impurities, or boundaries is established in the framework of the nonperturbative phenomenon of dynamical chiral symmetry breaking in the system of (2+1)-dimensional Dirac-like nodal quasiparticles. We determine the critical exponents and quasiparticle spectral functions that characterize the corresponding quantum-critical behavior and discuss some of its potentially observable spectral and transport features.

Effective Lorentz force due to small-sngle impurity scattering: magnetotransport in high- Tc superconductors

We show that a scattering rate which varies with angle around the Fermi surface has the same effect as a periodic Lorentz force on magnetotransport coefficients. This effect, together with the marginal Fermi liquid inelastic scattering rate, gives a quantitative explanation of the temperature dependence and the magnitude of the observed Hall effect and magnetoresistance with just the measured zero-field resistivity as input.

Evidence of electron fractionalization from photoemission spectra in the high temperature superconductors

In the normal state of the high temperature superconductors Bi(2)Sr(2)CaCu(2)O(8+delta) and La2(-x)Sr(x)CuO4, and in the related "stripe ordered" material, La(1.25)Nd(0.6)Sr(0.15)CuO4, there is sharp structure in the measured single hole spectral function, A<(k-->,omega), considered as a function of k--> at fixed small binding energy omega. At the same time, as a function of omega at fixed k--> on much of the putative Fermi surface, any structure in A<(k-->,omega), other than the Fermi cutoff, is very broad. This is characteristic of the situation in which there are no stable excitations with the quantum numbers of the electron, as is the case in the one-dimensional electron gas.

Observation of d(x2-y2)-like superconducting gap in an electron-doped high-temperature superconductor

High-resolution angle-resolved photoemission spectroscopy of the electron-doped high-temperature superconductor Nd(2-x)Ce(x)CuO4 (x = 0.15, transition temperature T(c) = 22 K) has found the quasiparticle signature as well as the anisotropic d(x2-y2)-like superconducting gap. The spectral line shape at the superconducting state shows a strong anisotropic nature of the many-body interaction. The result suggests that the electron-hole symmetry is present in the high-temperature superconductors.

Renormalization of spectral line shape and dispersion below Tc in Bi2Sr2CaCu2O8+delta

Angle-resolved photoemission data in the superconducting state of Bi2Sr2CaCu2O8+delta show a kink in the dispersion along the zone diagonal, which is related via a Kramers-Krönig analysis to a drop in the low energy scattering rate. As one moves towards (pi,0), this kink evolves into a spectral dip. The occurrence of these anomalies in the dispersion and line shape throughout the zone indicates the presence of a new energy scale in the superconducting state.

Giant enhancement of the thermal Hall conductivity kappa(xy) in the superconductor YBa(2)Cu(3)O(7)

In high-purity YBa(2)Cu(3)O(7), the (weak-field) thermal Hall conductivity kappa(xy) is observed to increase a thousand-fold between 90 and 30 K. The inferred quasiparticle lifetime tau increases a hundred-fold starting below 90 K, in disagreement with a recent photoemission experiment. We show that kappa(xy) exhibits a specific scaling behavior below approximately 30 K. This scaling may bear on the issue of whether Landau quantization of the quasiparticle states occurs.

Marginal Fermi liquid resonance induced by a quantum magnetic impurity in d-wave superconductors

We consider a model of an Anderson impurity embedded in a d(x(2)-y(2))--wave superconducting state to describe the low-energy excitations of cuprate superconductors doped with a small amount of magnetic impurities. Because of the Dirac-like energy dispersion, a sharp localized resonance above the Fermi energy, showing a marginal Fermi liquid behavior ( omega ln omega as omega-->0), is predicted for the impurity states. The same logarithmic dependence of self-energy and a linear frequency dependence of the relaxation rate are also derived for the conduction electrons, characterizing a new universality class for the strong coupling fixed point. At the resonant energies, the spatial distribution of the electron density of states around the magnetic impurity is also calculated.

Quantum phase transitions in d-wave superconductors

Motivated by the strong, low temperature damping of nodal quasiparticles observed in some cuprate superconductors, we study quantum phase transitions in d(x(2)-y(2)) superconductors with a spin-singlet, zero momentum, fermion bilinear order parameter. We present a complete, group-theoretic classification of such transitions into seven distinct cases (including cases with nematic order) and analyze fluctuations by the renormalization group. We find that only two, the transitions to d(x(2)-y(2))+is and d(x(2)-y(2))+id(xy) pairing, possess stable fixed points with universal damping of nodal quasiparticles; the latter leaves the gapped quasiparticles along (1,0), (0,1) essentially undamped.

Neutron resonance: modeling photoemission and tunneling data in the superconducting state of Bi2Sr2CaCu2O8+delta

Motivated by neutron scattering data, we develop a model of electrons interacting with a magnetic resonance and use it to analyze angle resolved photoemission and tunneling data in the superconducting state of Bi(2)Sr(2)CaCu(2)O(8+delta). We not only can explain the peak-dip-hump structure observed near the (pi,0) point, and its particle-hole asymmetry as seen in superconductor-insulator-normal tunneling spectra, but also its evolution throughout the Brillouin zone, including a velocity "kink" near the d-wave node.

Evidence for an energy scale for quasiparticle dispersion in Bi2Sr2CaCu2O8

Quasiparticle dispersion in Bi2Sr2CaCu2O8 is investigated with improved angular resolution as a function of temperature and doping. Unlike the linear dispersion predicted by the band calculation, the data show a sharp break in dispersion at 50+/-15 meV binding energy where the velocity changes by a factor of 2 or more. This change provides an energy scale in the quasiparticle self-energy. This break in dispersion is evident at and away from the d-wave node line, but the magnitude of the dispersion change decreases with temperature and with increasing doping.

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).

Fermi surface of Bi2Sr2CaCu2O8

We study the Fermi surface of Bi2Sr2CaCu2O8 using angle resolved photoemission spectroscopy (ARPES) with a momentum resolution of approximately 0.01 of the Brillouin zone. We show that, contrary to recent suggestions, the ARPES derived Fermi surface is a large hole barrel centered at (pi,pi), independent of the incident photon energy. We caution that the photon energy and k dependence of the matrix elements, if not properly accounted for, can lead to misinterpretation of ARPES intensities.

Advances in the physics of high-temperature superconductivity

The high-temperature copper oxide superconductors are of fundamental and enduring interest. They not only manifest superconducting transition temperatures inconceivable 15 years ago, but also exhibit many other properties apparently incompatible with conventional metal physics. The materials expand our notions of what is possible, and compel us to develop new experimental techniques and theoretical concepts. This article provides a perspective on recent developments and their implications for our understanding of interacting electrons in metals.