Sakai, Civelli and Imada (Phys. Rev. Lett. 116, 057003 (2016)) proposed, from a one-to-one correspondence between cellular dynamical mean-field theory solutions of the two-dimensional Hubbard model and an effective two-component fermion model, that a hidden fermion — a fermionic excitation emerging from strong correlations rather than a bare band — hybridizes with the quasiparticles of the cuprate CuO2_2 planes and thereby both generates the pseudogap and strongly enhances dd-wave Cooper pairing, in contrast to pairing mediated by a bosonic glue such as spin fluctuations. The problem the paper leaves open is: identify the microscopic origin and operator identity of the hidden fermion (a composite local fermion versus an antiferromagnetic band-folded copy of the electron, or a mixture), establish whether the hybridization mechanism survives dopant-induced disorder and multiband/multilayer complexity across cuprate families, determine its relation to proposed quantum criticalities and competing orders, and identify the two-particle response signatures that would unambiguously discriminate hidden-fermion dynamics from bosonic-glue scenarios. Follow-up work through 2026 — machine-learning extraction of hidden self-energy peaks, RIXS exciton anomalies, and a unified ARPES/quasiparticle-interference analysis — has produced mounting but contested support, while fermion-boson (glue) theories reproduce part of the same phenomenology; the identification and discrimination core remains open.

Background

Cuprate high-temperature superconductors consist of CuO2_2 planes whose parent compounds are antiferromagnetic Mott insulators — insulators in which electron localization is caused by the strong on-site Coulomb repulsion UU rather than by band filling. Hole doping converts them into superconductors with transition temperatures up to about 134 K at ambient pressure, passing through a puzzling pseudogap regime in which the electronic spectrum near the antinodal momenta (π,0)(\pi,0) and (0,π)(0,\pi) is depleted already well above TcT_c. The superconducting order parameter is of dd-wave symmetry, meaning it changes sign under a 90-degree in-plane rotation and has gap maxima at the antinodes. In conventional superconductors, Cooper pairing is mediated by a bosonic glue — phonons in BCS–Eliashberg theory — and the leading glue candidates proposed for the cuprates were spin fluctuations; in an Eliashberg picture the glue appears as a peak in the imaginary part of the electron self-energy Σ(ω)\Sigma(\omega) at the boson energy.

Sakai, Civelli and Imada (Phys. Rev. Lett. 116, 057003 (2016)), building on earlier cluster studies of the dynamical pairing interaction by Civelli (Phys. Rev. Lett. 103, 136402 (2009)), studied the two-dimensional Hubbard model with cellular dynamical mean-field theory (CDMFT) — a cluster quantum-embedding method that treats local and short-range correlations of the lattice model numerically essentially exactly within a finite cluster. They found a one-to-one correspondence between the CDMFT self-energies and an effective two-component fermion model in which the quasiparticle ckc_{\mathbf k} hybridizes, with amplitude VV, with a hidden fermion fkf_{\mathbf k} — a fermionic excitation that is not a bare band of the model but emerges from the strong correlations. Schematically, the single-particle Green's function takes the form

G−1(k,ω)=ω+μ−εk−∣V∣2ω−εf(k)−Σano(k,ω),G^{-1}(\mathbf k,\omega)=\omega+\mu-\varepsilon_{\mathbf k}-\frac{|V|^2}{\omega-\varepsilon_f(\mathbf k)}-\Sigma^{\mathrm{ano}}(\mathbf k,\omega),

where the pole-form hybridization term plays the role of the normal self-energy Σnor\Sigma^{\mathrm{nor}} and simultaneously boosts the anomalous self-energy Σano\Sigma^{\mathrm{ano}} that carries the superconducting gap (in the source paper's two-component model the hybridization amplitude is denoted VV, with Δ\Delta reserved for the superconducting gap function; Σano\Sigma^{\mathrm{ano}} enters off-diagonally in the Nambu representation, and the scalar pole term above corresponds to the limit of vanishing hidden-fermion pairing amplitude DfD_f). The same hidden fermion generates the pseudogap above TcT_c, giving the two phenomena a common origin — in contrast to a glue scenario, in which pairing is mediated by a retarded bosonic interaction. A crucial subtlety is that the poles of Σnor\Sigma^{\mathrm{nor}} and Σano\Sigma^{\mathrm{ano}} cancel in G−1G^{-1}, so the hidden fermion is essentially invisible in single-particle spectra such as angle-resolved photoemission spectroscopy (ARPES), and discriminating signatures must instead be sought in two-particle responses — for example quasiparticle interference (QPI, the standing-wave patterns imaged by scanning tunneling microscopy that encode the momentum structure of the density response), resonant inelastic X-ray scattering (RIXS), or optical conductivity.

The paper proposes two candidate microscopic realizations of ff: an antiferromagnetic band-folded copy of the electron, ck+Qc_{\mathbf k+\mathbf Q} with Q=(π,π)\mathbf Q=(\pi,\pi) as in mean-field antiferromagnetism, and a composite local operator f~\tilde f built from the electron operator and the local density — the composite fermion earlier introduced by Yamaji and Imada (Phys. Rev. B 83, 214522 (2011)) to describe the incoherent part of the electron spectrum. The strong electron–hole asymmetry of the computed ImΣnor\Sigma^{\mathrm{nor}} implies a positive hidden-fermion dispersion εf>0\varepsilon_f>0 at the antinodal momentum, which favors the composite-fermion candidate but does not settle the question. Subsequent developments sharpen the stakes: machine-learning extraction of the normal and anomalous self-energies from ARPES data found hidden peak structures that dominate the superconducting gap (Yamaji et al., Phys. Rev. Research 3, 043099 (2021)); RIXS found an excitonic two-particle anomaly tied to the superconducting onset (Singh et al., Nature Communications 13 (2022)); and a unified analysis of ARPES and QPI data reported that the two-component model reproduces both simultaneously, including a measured QPI signature distinct from the single-component prediction, while predicting a further unoccupied-side signature (Sakai et al., Phys. Rev. X 16, 011018 (2026)). At the same time, Chubukov and Schmalian (Phys. Rev. B 101, 180510 (2020)) showed that fermion–boson (glue) theories can generate cancelling peak structures in the two self-energy components as well, so the observed phenomenology does not yet uniquely select the hidden-fermion mechanism.

Problem Statement

Determine whether a hidden fermion — a fermionic excitation emerging from strong electron correlations rather than a bare band — hybridizes with the quasiparticles of the CuO2_2 planes and thereby generates both the pseudogap and the strongly bound dd-wave Cooper pairs of the cuprates, by settling the four linked issues that Sakai, Civelli and Imada (Phys. Rev. Lett. 116, 057003 (2016)) left open:

(i) Microscopic identification: derive, from a microscopic Hamiltonian (the two-dimensional Hubbard model or ab initio downfolded cuprate Hamiltonians), which excitation actually hybridizes with the quasiparticles in the doped cuprates — the composite local fermion f~\tilde f, the antiferromagnetic band-folded copy ck+Qc_{\mathbf k+\mathbf Q} with Q=(π,π)\mathbf Q=(\pi,\pi), a mixture, or another realization — and whether the same realization operates across the different cuprate families.

(ii) Robustness and generality: establish whether the hybridization-based pairing enhancement persists in the presence of dopant-induced spatial randomness (in particular whether hidden fermions form large local gaps that enhance superconductivity by the proximity effect — the induction of a superconducting gap in one region through contact with a neighboring, strongly paired one), in multi-band and multilayer materials, and across the parameter regimes relevant to the different cuprate families.

(iii) Relation to other proposed phenomena: determine how the hidden-fermion mechanism connects to the quantum criticalities — continuous phase transitions occurring at zero temperature — and competing-order scenarios that have been proposed in the cuprate phase diagram.

(iv) Experimental detection: derive concrete two-particle response signatures — for example in quasiparticle interference, resonant inelastic X-ray scattering, or optics — that unambiguously discriminate hidden-fermion dynamics from bosonic-glue pairing, and, where published two-particle data permit, validate those signatures against the measurements.

The single scientific objective uniting these facets is to establish — or refute — the hidden-fermion mechanism as the origin of high-temperature superconductivity and the pseudogap in the cuprates: the microscopic identification (i) fixes which signatures the experiments (iv) must look for, the robustness tests (ii) decide whether the mechanism identified in model calculations operates in the real materials, and (iii) locates the mechanism within the phase diagram alongside the criticality and competing-order phenomenology. The problem is complete when the mechanism is either established in the real cuprates — which requires the microscopic identification (i) of the hybridizing excitation together with the discriminating two-particle signature (iv), with the robustness tests (ii) confirming that the identified mechanism operates in the real materials — or refuted by conclusive experimental or numerical evidence that rules out a hybridization mechanism of the above form; for (iv) a derived discriminating signature — validated against the published two-particle measurements where such data permit, but not requiring a new measurement — suffices; the relation to proposed quantum criticalities and competing orders (iii) locates an established mechanism within the phase diagram and is not separately required for completion.

References

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