Scanning-tunneling experiments on optimally-to-overdoped Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta} (Bi2212) showed that the local superconducting pairing strength is predicted not by local electron–boson coupling in the 20–120 meV window, which shows no correlation with the local gap, but by high-energy (up to ~400 meV), strongly electron–hole-asymmetric, hole-like excitations of the normal state — in particular a tunneling 'hump' near −150 to −300 meV whose position tracks the eventual gap. The unresolved problem is to identify the microscopic origin of these excitations and hence of the inhomogeneous pairing interaction: asymmetric or high-energy (>120 meV) bosonic spectra, band-structure effects including bilayer splitting, or intrinsic correlations of a doped Mott insulator; to determine how these atomic-scale spectroscopic features and their correlation with pairing evolve with doping and temperature; and to disentangle extrinsic structural/chemical inhomogeneity from intrinsic electronic correlations. Later work has advanced each front (atomic manipulation, underdoped spectroscopy, glue spectroscopy) but no consensus resolution exists; the core discrimination remains open.

Background

The cuprate high-temperature superconductors are layered copper oxides that become superconducting when holes or electrons are doped into antiferromagnetic Mott-insulating parent compounds (a Mott insulator is an insulator blocked by electron–electron repulsion rather than by filled bands). In Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta} (Bi2212), scanning tunneling spectroscopy (STS) — measuring the differential conductance dI/dV of electrons tunneling from a sharp tip, which tracks the local density of electronic states — reveals that the superconducting energy gap varies by tens of meV on nanometer length scales. This 'gap inhomogeneity' raised a mechanistic question: what locally sets the pairing strength?

In conventional superconductors, tunneling spectroscopy diagnosed the pairing mechanism through strong-coupling features (dips and humps in dI/dV at energies just beyond the gap) that reflect the exchange of bosonic quanta — phonons — binding the Cooper pairs, allowing the bosonic spectrum to be inferred from the measured conductance. Applying the same logic to cuprates, several experiments reported mode-like features in the 20–120 meV range, attributed to phonons or to the ~40 meV magnetic resonance (a collective spin-excitation mode of the cuprate superconducting state observed in neutron scattering). A bosonic pairing 'glue' would predict that locations with stronger local electron–boson coupling develop larger gaps.

Pasupathy et al. (Science 320, 196 (2008)) tested this directly with lattice-tracking STS: repeated spectroscopic maps on the same atomic sites from ~10 K to ~90 K in overdoped (hole doping x ≈ 0.24, T_c = 62 K) and optimally doped Bi2212. Above ~90 K the superconducting gaps have collapsed everywhere, but the normal-state spectra remain spatially inhomogeneous, gapless, and strongly asymmetric between electron and hole bias. Two systematics emerged. First, the local strength of electron–boson coupling to modes in the 20–120 meV window, and the local boson energies, do not correlate with the local gap magnitude or its onset temperature — so low-energy bosons cannot cause the gap variation. Second, the normal-state Fermi-level conductance anticorrelates with the low-temperature gap (correlation ≈ −0.75), and the position of a hole-side 'hump' between −150 and −300 meV shifts systematically with the eventual gap: regions with lower normal-state conductance nucleate larger superconducting gaps.

What could these high-energy asymmetric excitations be? The paper lists three candidate origins, none excluded. (i) Coupling to a highly asymmetric spectrum of bosonic excitations such as spin fluctuations (quantized collective spin fluctuations of the antiferromagnetic correlations); this requires the candidate bosons to couple very asymmetrically to electron versus hole tunneling. (ii) Band-structure effects, notably bilayer splitting — Bi2212 has two CuO2_2 planes per unit cell whose bonding and antibonding combinations split the electronic bands; however, a smooth non-interacting band structure struggles to explain the strong atomic-scale spatial variation of the features. (iii) Intrinsic excitations of a doped Mott insulator, where strong Coulomb repulsion naturally makes electron and hole excitations asymmetric; plaquette dynamical mean-field theory (a cluster extension of dynamical mean-field theory, the method that treats a lattice quantum problem by self-consistently embedding a small cluster) by Haule and Kotliar indeed produces a hole-side hump that correlates with pairing strength, and Anderson's projected-Fermi-liquid picture — a Fermi liquid modified to exclude doubly occupied sites, as in the parent Mott insulator — gives a related account. Complicating the interpretation, structural supermodulation (the periodic lattice distortion along one in-plane axis) correlates ~10% with the normal-state conductance maps, and dopant-atom-induced resonances near −900 meV correlate ~30%, so extrinsic structural/chemical disorder demonstrably contributes alongside whatever intrinsic correlations exist. These facts frame the open question below, which is the central experimental discriminator for the cuprate pairing mechanism in this material.

Problem Statement

For Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta}, determine the microscopic origin of the normal-state electronic excitations that set the strength and spatial variation of the superconducting pairing interaction, jointly resolving the three issues left open by the lattice-tracking tunneling study of Pasupathy et al. (Science 320, 196 (2008)): (1) identify whether the high-energy (up to ~400 meV), strongly electron–hole-asymmetric hole-like excitations — including the normal-state tunneling hump between −150 and −300 meV whose position tracks the eventual local gap, and the anticorrelation (≈ −0.75) between normal-state Fermi-level conductance and low-temperature gap — arise from coupling to an asymmetric bosonic spectrum, from band-structure effects such as bilayer splitting, or from intrinsic correlations of a doped Mott insulator, and establish which mechanism the evidence singles out; (2) determine how these atomic-scale normal-state spectroscopic features and their correlation with pairing evolve across the phase diagram as a function of hole doping (including the underdoped regime, where the pseudogap — a partial depletion of low-energy electronic states that persists above the superconducting transition temperature — develops) and at higher temperatures; and (3) quantitatively decompose how much of the variation of local electronic excitations and gaps is set by extrinsic structural/chemical inhomogeneity (supermodulation, dopant-induced resonances, local lattice configuration) versus intrinsic electronic correlations. These components jointly discriminate the pairing mechanism of the cuprates: a single microscopic account should simultaneously explain the gap magnitudes, their onset temperatures, the normal-state hump systematics, the electron–hole asymmetry, and the non-correlation (or correlation) of bosonic features with local pairing strength.

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