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)).