Time- and frequency-resolved optical spectroscopy of optimally doped Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta} showed that the frequency-dependent bosonic function Π(Ω)\Pi(\Omega) that 'glues' Cooper pairs together is dominated by excitations of electronic origin (coupling λbe≈1.1\lambda_{\text{be}}\approx 1.1), sufficient by itself to account for the high superconducting transition temperature, while phononic channels are too weak (λSCP≈0.4\lambda_{\text{SCP}}\approx 0.4, λlat≈0.2\lambda_{\text{lat}}\approx 0.2). The source work, however, could not identify what the electronic excitations actually are — antiferromagnetic spin fluctuations, loop currents, or other collective modes — nor exclude a cooperative phononic role, contributions above the 1 eV analysis cutoff, or an underestimate of the electronic coupling due to its 300 K determination. A decade of follow-up work across optical, tunneling, Raman, photoemission, and theoretical routes has produced competing partial identifications but no unambiguous one. The open problem is the quantitative, experimentally grounded identification of the electronic bosonic excitations that mediate high-temperature superconductivity in the cuprates, together with the precise interplay of the electron-phonon channel in the superconducting transition.

Background

In a superconductor, electrons form Cooper pairs below a critical temperature TcT_c, and in conventional (BCS–Eliashberg) superconductors the attractive 'glue' that binds them is provided by phonons, the quantized vibrations of the crystal lattice. In the cuprate high-TcT_c superconductors — layered copper oxides, of which Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta} (Bi2212) is a workhorse example and whose record transition temperatures reach ~135 K at ambient pressure (in the mercury-based family; ~92 K in optimally doped Bi2212) — phonons appear too weak, and the leading candidates are collective excitations generated by the strongly correlated electrons themselves. A useful model-independent way to characterize the glue is the bosonic function Π(Ω)\Pi(\Omega), the frequency-dependent spectrum of bosons that scatter charge carriers; in Eliashberg-type theories it enters the quasiparticle self-energy, and its strength is summarized by a mass-enhancement coupling constant λ\lambda. In conventional superconductors this object is extracted from tunneling or optical data, but in cuprates electronic and phononic contributions overlap in energy, making an equilibrium decomposition ambiguous. Dal Conte et al. (Science 335, 1600, 2012) bypassed this by broadband femtosecond pump-probe optical spectroscopy on optimally doped Bi2212: after a laser pulse breaks pairs, the electronic and phononic contributions to Π(Ω)\Pi(\Omega) recover on different timescales, allowing them to be disentangled in the time domain. They found the electronic component Πbe(Ω)\Pi_{\text{be}}(\Omega) spread up to the 1 eV analysis cutoff with coupling λbe≈1.1\lambda_{\text{be}}\approx 1.1 — enough, through an extended version of the McMillan formula (the standard empirical relation that estimates TcT_c from a coupling strength and a characteristic boson energy) adapted to dd-wave pairing, to account for the high TcT_c on its own — while the phononic channels are weaker (λSCP≈0.4\lambda_{\text{SCP}}\approx 0.4 for the strongly-coupled phonons, the small subset of phonon modes — prominently the buckling and breathing copper–oxygen vibrations — that carry a disproportionate share of the coupling, and λlat≈0.2\lambda_{\text{lat}}\approx 0.2 for all other lattice modes), a decomposition consistent with the small isotope effect (the shift of spectroscopic features when 16^{16}O is replaced by the heavier 18^{18}O) observed in photoemission. Two families of electronic excitations are the canonical candidates: antiferromagnetic spin fluctuations (fluctuating remnants of the parent compound's magnetic order, often called paramagnons), and 'loop currents' — persistent circulating charge currents proposed to fluctuate in the pseudogap phase, the enigmatic partially gapped state that cuprates enter well above TcT_c. The experiment measured the total electronic glue but could not distinguish between these, and it left open whether the electron-phonon channel, while too weak to set TcT_c, still cooperates in the superconducting transition; whether the electronic glue extends above 1 eV; and how the 300 K determination of λbe\lambda_{\text{be}} understates the electronic pairing strength as the pseudogap develops on cooling toward TcT_c.

Problem Statement

What is the microscopic nature of the electronic bosonic excitations that dominate the glue function Π(Ω)\Pi(\Omega) of the cuprate high-TcT_c superconductors — are they predominantly antiferromagnetic spin fluctuations, loop currents of the pseudogap phase, other collective modes, or a combination — and how do these electronic channels quantitatively interplay with the electron-phonon channel in producing the superconducting transition? A complete answer must: (i) identify the excitations unambiguously, through evidence that discriminates among the candidate modes (e.g., momentum-, energy-, temperature-, doping-, and fluence- (laser pulse energy density) resolved spectroscopy or controlled theoretical calculation) rather than trend associations; (ii) assign quantitative coupling strengths to each channel and determine whether electron-phonon coupling cooperates in, is irrelevant to, or opposes the transition, checking consistency with the observed TcT_c, the isotope effect, and the temperature dependence of the electronic component as the pseudogap develops on cooling from 300 K toward TcT_c (where the original 300 K analysis is expected to underestimate the electronic contribution); and (iii) establish whether contributions to Π(Ω)\Pi(\Omega) above the 1 eV cutoff of the original analysis are negligible or materially modify the coupling constants. These facets jointly serve one objective — a quantitative, experimentally grounded microscopic identification of the cuprate pairing glue — and an answer that resolves the identification while leaving its quantitative interplay undetermined is partial. Facets (i)–(iii) are each independently required, and for facet (i) 'unambiguous' means that the identification rests on evidence that separates the candidate modes rather than on association with a single doping or energy trend, and that it states which candidate(s) remain and why the competing modes are excluded or disfavoured.

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