Energy-dependent enhancement of the electron-coupling spectrum of the underdoped Bi2Sr2CaCu2O(8+δ) superconductor

Unveiling phase diagram of the lightly doped high-Tc cuprate superconductors with disorder removed

The currently established electronic phase diagram of cuprates is based on a study of single- and double-layered compounds. These CuO₂ planes, however, are directly contacted with dopant layers, thus inevitably disordered with an inhomogeneous electronic state. Here, we solve this issue by investigating a 6-layered Ba₂Ca₅Cu₆O₁₂(F,O)₂ with inner CuO₂ layers, which are clean with the extremely low disorder, by angle-resolved photoemission spectroscopy (ARPES) and quantum oscillation measurements. We find a tiny Fermi pocket with a doping level less than 1% to exhibit well-defined quasiparticle peaks which surprisingly lack the polaronic feature. This provides the first evidence that the slightest amount of carriers is enough to turn a Mott insulating state into a metallic state with long-lived quasiparticles. By tuning hole carriers, we also find an unexpected phase transition from the superconducting to metallic states at 4%. Our results are distinct from the nodal liquid state with polaronic features proposed as an anomaly of the heavily underdoped cuprates.

Translational-Invariant Bipolarons and Superconductivity

A translation-invariant (TI) bipolaron theory of superconductivity based, like Bardeen–Cooper–Schrieffer theory, on Fröhlich Hamiltonian is presented. Here the role of Cooper pairs belongs to TI bipolarons which are pairs of spatially delocalized electrons whose correlation length of a coupled state is small. The presence of Fermi surface leads to the stabilization of such states in its vicinity and a possibility of their Bose–Einstein condensation (BEC). The theory provides a natural explanation of the existence of a pseudogap phase preceding the superconductivity and enables one to estimate the temperature of a transition T * from a normal state to a pseudogap one. It is shown that the temperature of BEC of TI bipolarons determines the temperature of a superconducting transition T c which depends not on the bipolaron effective mass but on the ordinary mass of a band electron. This removes restrictions on the upper limit of T c for a strong electron-phonon interaction. A natural explanation is provided for the angular dependence of the superconducting gap which is determined by the angular dependence of the phonon spectrum. It is demonstrated that a lot of experiments on thermodynamic and transport characteristics, Josephson tunneling and angle-resolved photoemission spectroscopy (ARPES) of high-temperature superconductors does not contradict the concept of a TI bipolaron mechanism of superconductivity in these materials. Possible ways of enhancing T c and producing new room-temperature superconductors are discussed on the basis of the theory suggested.

A New Landscape of Multiple Dispersion Kinks in a High-T c Cuprate Superconductor

Conventional superconductivity is caused by electron-phonon coupling. The discovery of high-temperature superconductors raised the question of whether such strong electron-phonon coupling is realized in cuprates. Strong coupling with some collective excitation mode has been indicated by a dispersion “kink”. However, there is intensive debate regarding whether the relevant coupling mode is a magnetic resonance mode or an oxygen buckling phonon mode. This ambiguity is a consequence of the energy of the main prominent kink. Here, we show a new landscape of dispersion kinks. We report that heavily overdoping a Bi₂Sr₂CaCu₂O_8+δ superconductor results in a decline of the conventional main kink and a rise of another sharp kink, along with substantial energy shifts of both. Notably, the latter kink can be ascribed only to an oxygen-breathing phonon. Hence, the multiple phonon branches provide a consistent account of our data set on the multiple kinks. Our results suggest that strong electron-phonon coupling and its dramatic change should be incorporated into or reconciled with scenarios for the evolution of high-T_c superconductivity.

Sharp low-energy feature in single-particle spectra due to forward scattering in d-wave cuprate superconductors

There is an enormous interest in the renormalization of the quasiparticle (qp) dispersion relation of cuprate superconductors both below and above the critical temperature T_{c} because it enables the determination of the fluctuation spectrum to which the qp's are coupled. A remarkable discovery by angle-resolved photoemission spectroscopy (ARPES) is a sharp low-energy feature (LEF) in qp spectra well below the superconducting energy gap but with its energy increasing in proportion to T_{c} and its intensity increasing sharply below T_{c}. This unexpected feature needs to be reconciled with d-wave superconductivity. Here, we present a quantitative analysis of ARPES data from Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} (Bi2212) using Eliashberg equations to show that the qp scattering rate due to the forward scattering impurities far from the Cu-O planes is modified by the energy gap below T_{c} and shows up as the LEF. This is also a necessary step to analyze ARPES data to reveal the spectrum of fluctuations promoting superconductivity.

Doping dependence of low-energy quasiparticle excitations in superconducting Bi2212

: The doping-dependent evolution of the d-wave superconducting state is studied from the perspective of the angle-resolved photoemission spectra of a high-Tc cuprate, Bi2Sr2CaCu2 O8+δ (Bi2212). The anisotropic evolution of the energy gap for Bogoliubov quasiparticles is parametrized by critical temperature and superfluid density. The renormalization of nodal quasiparticles is evaluated in terms of mass enhancement spectra. These quantities shed light on the strong coupling nature of electron pairing and the impact of forward elastic or inelastic scatterings. We suggest that the quasiparticle excitations in the superconducting cuprates are profoundly affected by doping-dependent screening.

Anomalous doping variation of the nodal low-energy feature of superconducting (Bi,Pb)2(Sr,La)2CuO(6+δ) crystals revealed by laser-based angle-resolved photoemission spectroscopy

The nodal band dispersion in (Bi,Pb)(2)(Sr,La)(2)CuO(6+δ) (Bi2201) is investigated over a wide range of doping by using 7-eV laser-based angle-resolved photoemission spectroscopy. We find that the low-energy band renormalization ("kink"), recently discovered in Bi(2)Sr(2)CaCu(2)O(8+δ) (Bi2212), also occurs in Bi2201, but at a binding energy around half that in Bi2212. Surprisingly, the coupling energy dramatically increases with a decrease of carrier concentration, showing a sharp enhancement across the optimal doping. These properties (material and doping dependence of the coupling energy) demonstrate the significant correlation among the mode coupling, the energy gap close to the node, and the strong electron correlation. Our results suggest forward scattering arising from the interplay between the electrons and in-plane polarized acoustic phonon branch as the origin of the low-energy renormalization.

Relation between the nodal and antinodal gap and critical temperature in superconducting Bi2212

An energy gap is, in principle, a dominant parameter in superconductivity. However, this view has been challenged for the case of high-T_c cuprates, because anisotropic evolution of a d-wave-like superconducting gap with underdoping has been difficult to formulate along with a critical temperature T_c. Here we show that a nodal-gap energy 2Δ_N closely follows 8.5 k_BT_c with underdoping and is also proportional to the product of an antinodal gap energy Δ^* and a square-root superfluid density √P_s for Bi₂Sr₂CaCu₂O_8+δ, using low-energy synchrotron-radiation angle-resolved photoemission. The quantitative relations imply that the distinction between the nodal and antinodal gaps stems from the separation of the condensation and formation of electron pairs, and that the nodal-gap suppression represents the substantial phase incoherence inherent in a strong-coupling superconducting state. These simple gap-based formulae reasonably describe a crucial part of the unconventional mechanism governing T_c.

In conventional superconductors, the critical temperature is proportional to the superconducting energy gap, but this is not so in unconventional superconductors. Anzai et al. identify an alternative relationship involving nodal and antinodal gaps in an underdoped cuprate superconductor.

Towards resolution of the Fermi surface in underdoped high-Tc superconductors

We survey recent experimental results including quantum oscillations and complementary measurements probing the electronic structure of underdoped cuprates, and theoretical proposals to explain them. We discuss quantum oscillations measured at high magnetic fields in the underdoped cuprates that reveal a small Fermi surface section, comprising quasiparticles that obey Fermi-Dirac statistics, unaccompanied by other states of comparable thermodynamic mass at the Fermi level. The location of the observed Fermi surface section at the nodes is indicated by a body of evidence including the collapse in Fermi velocity measured by quantum oscillations, which is found to be associated with the nodal density of states observed in angular resolved photoemission, the persistence of quantum oscillations down to low fields in the vortex state, the small value of density of states from heat capacity and the multiple frequency quantum oscillation pattern consistent with nodal magnetic breakdown of bilayer-split pockets. A nodal Fermi surface pocket is further consistent with the observation of a density of states at the Fermi level concentrated at the nodes in photoemission experiments, and the antinodal pseudogap observed by photoemission, optical conductivity, nuclear magnetic resonance (NMR) Knight shift, as well as other complementary diffraction, transport and thermodynamic measurements. One of the possibilities considered is that the small Fermi surface pockets observed at high magnetic fields can be understood in terms of Fermi surface reconstruction by a form of small wavevector charge order, observed over long lengthscales in experiments such as NMR and x-ray scattering, potentially accompanied by an additional mechanism to gap the antinodal density of states.

Evidence for the importance of extended Coulomb interactions and forward scattering in cuprate superconductors

The prevalent view of the high-temperature superconducting cuprates is that their essential low-energy physics is captured by local Coulomb interactions. However, this view been challenged recently by studies indicating the importance of longer-range components. Motivated by this, we demonstrate the importance of these components by examining the electron-phonon (e-ph) interaction with acoustic phonons in connection with the recently discovered renormalization in the near-nodal low-energy (~8-15 meV) dispersion of Bi(2)Sr(2)CaCu(2)O(8+δ). By studying its nontrivial momentum and doping dependence we conclude a predominance of forward scattering arising from the direct interplay between the e-ph and extended Coulomb interactions. Our results thus demonstrate how the low-energy renormalization can provide a pathway to new insights into how these interactions interplay with one another and influence pairing and dynamics in the cuprates.

Quantum oscillations in the high-Tc cuprates

We review recent progress in the study of quantum oscillations as a tool for uniquely probing low-energy electronic excitations in high-T(c) cuprate superconductors. Quantum oscillations in the underdoped cuprates reveal that a close correspondence with Landau Fermi-liquid behaviour persists in the accessed regions of the phase diagram, where small pockets are observed. Quantum oscillation results are viewed in the context of momentum-resolved probes such as photoemission, and evidence examined from complementary experiments for potential explanations for the transformation from a large Fermi surface into small sections. Indications from quantum oscillation measurements of a low-energy Fermi surface instability at low dopings under the superconducting dome at the metal-insulator transition are reviewed, and potential implications for enhanced superconducting temperatures are discussed.