Quantitative material-specific foundations of polaron-bipolaron superconductivity in cuprates: effective interaction parameters, the BEC-Cooper crossover, and intrinsic pairing symmetry

The polaron-bipolaron theory proposes that high-temperature superconductivity in cuprates arises from strong coupling of charge carriers to low-energy phonons, with superconductivity described either as Bose-Einstein condensation (BEC) of tightly bound inter-site bipolaron pairs or, when residual on-site polaronic repulsion is large, as Cooper-like pairing. G.-m. Zhao (arXiv:1307.4175, 2013) defended this theory, arguing that tunneling and photoemission data quantitatively confirm it; the open issue is whether the mechanism can be made quantitative and material-specific. Specifically, determine from measured material parameters the residual on-site polaronic repulsion $\tilde{U}$ and the effective electron-phonon coupling to low-energy phonons, map the resulting BEC-Cooper crossover, and establish through bulk-sensitive experiments across the full doping range whether the intrinsic pairing-gap symmetry differs from the d-wave condensate symmetry.

Background

In the cuprate high-temperature superconductors (layered copper oxides such as Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, 'Bi-2212'), superconductivity appears when charge carriers are doped into the CuO$_2$ planes, and the pairing mechanism has remained unsettled for decades. One long-standing minority program is the polaron-bipolaron theory. A polaron is an electronic charge carrier dressed by the lattice distortion it induces; when the coupling to lattice vibrations (the electron-phonon interaction, EPI) is strong, two polarons can bind into a bipolaron, a real-space bosonic pair. Depending on the range of the EPI (long-range Fröhlich coupling to polar optical modes versus short-range Holstein coupling), inter-site bipolarons can remain mobile enough to condense. In this picture the normal-state pseudogap (a partial suppression of low-energy spectral weight above $T_c$) is the polaron binding energy, and superconductivity is the Bose-Einstein condensation (BEC) of the pairs, in contrast to Bardeen-Cooper-Schrieffer (BCS) theory where pairing occurs in momentum space between electrons in a large Fermi surface (the surface enclosing the carrier count, testable by photoemission). Alexandrov, Samson, and Sica (Phys. Rev. B 85, 104520 (2012)) showed that a model with generic long-range Coulomb repulsion and Fröhlich EPI reduces, at very large lattice dielectric constant $\epsilon_0$, to a polaronic $t-J_p$ model in which the bare Coulomb repulsion and the EPI largely cancel; at realistic finite $\epsilon_0$ the cancellation is incomplete, leaving a residual on-site polaronic Hubbard repulsion $\tilde{U}$ whose size depends on the spatial extent of the Wannier orbitals (the localized orbital basis used to describe the CuO$_2$ bands). $\tilde{U}$ drives a crossover from BEC of inter-site bipolarons (small $\tilde{U}$, underdoped side) to Cooper-like pairing (large $\tilde{U}$, overdoped side), which is how the theory reconciles real-space pairing with the large Fermi surfaces seen in optimally doped and overdoped cuprates. Zhao's 2013 paper argued that tunneling humps and photoemission spectra are quantitatively consistent with this theory. First, the residual repulsion $\tilde{U}$ that the paper invokes (following Alexandrov-Samson-Sica) as the driver of the BEC-Cooper crossover has never been computed for a real material, so the crossover is not mapped. Second, as the paper's Sec. IV notes, first-principles (density-functional-based) calculations of the bare EPI conflict: local-density calculations find small couplings (Giustino, Cohen, and Louie, Nature 452, 975 (2008); Heid, Bohnen, Zeyher, and Manske, Phys. Rev. Lett. 100, 137001 (2008)), while inclusion of short-range Coulomb repulsion via LDA+$U$ (Zhang, Louie, and Cohen, Phys. Rev. Lett. 98, 067005 (2007)), nonadiabatic dynamical screening, or long-range couplings to c-axis phonons yields large couplings (Bauer and Falter, Phys. Rev. B 80, 094525 (2009)). Third, the superconducting condensate symmetry may differ from the intrinsic pairing-gap symmetry in the strong-coupling (local-pair) regime: phase-sensitive Josephson experiments (Tsuei and Kirtley, Rev. Mod. Phys. 72, 969 (2000)) establish a d-wave condensate (gap changing sign under 90-degree rotation), but the paper argues that such experiments probe surfaces and interfaces found to be intrinsically underdoped, and Zhao concluded from a finite gap along the diagonal direction in photoemission and from bulk Raman spectra that the intrinsic pairing gap is instead extended s-wave (sign-preserving but with eight nodal lines) in hole-doped and nodeless s-wave in electron-doped overdoped cuprates, presenting existing bulk-sensitive measurements as already decisive. That conclusion has not been adopted by later work, and a decisive bulk-sensitive test across the full doping range discriminating condensate symmetry from intrinsic pairing-gap symmetry is still lacking. For context, the polaron-bipolaron program is contested: the mainstream interpretation attributes pairing to repulsive electronic (spin-fluctuation) interactions with d-wave symmetry (see the review by Hashimoto, Vishik, He, Devereaux, and Shen, Nat. Phys. 10, 521 (2014)), so the quantitative program below would either establish the phononic account or falsify it against that alternative.

Problem Statement

The common objective is to make the polaron-bipolaron (strong electron-phonon-coupling) account of cuprate superconductivity quantitative, material-specific, and experimentally decisive. Concretely, from measured material parameters of the cuprates (static and high-frequency dielectric constants, Wannier-orbital sizes, phonon spectra, and bare Hubbard repulsion $U$): (a) compute quantitatively the effective low-energy polaronic Hamiltonian, in particular the residual on-site polaronic repulsion $\tilde{U}$ left by the incomplete cancellation of the bare Coulomb repulsion by the long-range Fröhlich electron-phonon interaction, and the effective coupling strengths to low-energy (roughly below 40 meV) phonon modes including polaronic density-of-states enhancement; (b) using these parameters, map the crossover between Bose-Einstein condensation of inter-site bipolarons and Cooper-like pairing as a function of dielectric screening, orbital size, and bare electron-phonon strength, and locate the underdoped, optimally doped, and overdoped cuprates on this map; (c) reconcile the conflicting first-principles magnitudes of the bare electron-phonon interaction by systematically including short-range Coulomb repulsion, nonadiabatic screening, and long-range (Fröhlich and c-axis) couplings, yielding robust material-specific bare coupling magnitudes; and (d) determine experimentally, with bulk-sensitive probes covering the full doping range, whether the symmetry of the superconducting condensate differs from the intrinsic pairing-gap symmetry (d-wave versus eight-node extended s-wave versus nodeless s-wave), resolving whether phase-sensitive surface experiments reflect only surface underdoping. Components (a)-(c) supply the effective theory and its parameters, and (d) supplies its independent experimental symmetry test. All four components are required jointly, and resolving one of them alone does not resolve the program: (a) is met by a numeric residual repulsion $\tilde{U}$ and an effective low-energy coupling strength for at least one named cuprate; (b) by the placement of a specific underdoped and a specific overdoped material on the crossover map; (c) by a settled bare first-principles electron-phonon magnitude for at least one material — this is the bare input that (a) dresses into its effective polaronic couplings, so (c) and (a) are distinct deliverables that must agree on a common material; and (d) by a determination of the intrinsic pairing-gap symmetry from bulk-sensitive measurements spanning the underdoped and overdoped regimes, where a documented determination from existing measurements resolves it whenever those measurements decisively discriminate the candidate symmetries, and otherwise the resolution must name the bulk-sensitive measurement that would decide it. Together they either establish the phononic mechanism quantitatively or falsify it.

References

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