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This paper presents a new theoretical framework that tries to describe three famous but different behaviors of cuprate superconductors from one starting point. The authors build a “relative-momentum-local” (RML) theory based on the t-J model, which models electrons constrained by strong repulsion and an antiferromagnetic (AFM) superexchange interaction. The idea is to follow how spin-singlet Cooper pairs (two electrons bound in a singlet state) respond at low energy, and to show that the same Cooper channel can organize into superconductivity (SC), a pseudogap (PG), or a strange metal (SM).
What the researchers did. They rewrote the AFM superexchange exactly in terms of Cooper-pair operators with a centre-of-mass momentum Q and a relative momentum q. They then defined two kinds of pair correlations: a block-resolved pair autocorrelation Pqq′ that probes pairs with the same relative momentum, and a collective channel correlation Cαα′ that detects macroscopic coherence in a symmetry channel (for example d-wave). Within a controlled set of approximations — notably the Gutzwiller approximation to enforce no double occupancy and two RML prescriptions (static and dynamic) — they solved or analyzed the resulting effective theories to extract single-particle and pair responses.
How the three states emerge in this view. Superconductivity appears when the collective d-wave correlation Cdd develops a sharp, zero-centre-of-mass-momentum singularity and a nonzero phase stiffness; that is, pairs become phase-coherent and static. The pseudogap appears when block-diagonal pair weight Pqq is enhanced but the collective mode remains broad and phase incoherent: this yields a solvable pseudogap Hamiltonian with nodal electron poles, antinodal gaps, resolution-broadened Fermi arcs (partial Fermi-surface features seen by angle-resolved photoemission spectroscopy, ARPES), and gapless charge-2e “Cooper surfaces.” The strange metal comes from dynamic, phase-incoherent pair fluctuations: finite centre-of-mass momentum particle-particle continua give Ohmic damping, and a dynamic RML treatment produces a one-loop fermion self-energy with marginal-Fermi-liquid (MFL) scaling (roughly a scattering rate linear in max(|ω|,kBT)).
Why this matters. The work offers a unified microscopic thread that links single-electron probes (ARPES), pair-sensitive probes, and thermodynamics within one Cooper-pair channel. It also makes concrete predictions that could test the picture. For example, a Cooper-surface Lifshitz transition in the model generates logarithmic enhancements in the specific heat coefficient and in charge response without producing a spin singularity. The authors propose that zero-energy ridges associated with Cooper surfaces would be a decisive experimental signature accessible to two-electron angle-resolved photoemission spectroscopy (2e-ARPES).
Important caveats and uncertainties. The RML theory relies on approximations: the Gutzwiller approximation to treat the no-double-occupancy constraint, static and dynamic RML prescriptions, Gaussian and one-loop treatments of fluctuations, and the assumption that the effective RML coupling is sufficiently isotropic and weakly temperature dependent to yield MFL scaling. These are controlled but still approximate steps. The predictions — such as gapless charge-2e Cooper surfaces and the 2e-ARPES signal — are theoretical and need experimental confirmation. The paper therefore offers a plausible unified route, but its applicability to real cuprates will rest on whether the proposed experimental signatures and thermodynamic trends are observed.