Unified Description of the Strange Metal, d-Wave Pairing, and Superconducting Dome in Cuprates from a Coherence Purity Principle
Kai Huang, Hongkui Liu, Ziwei Huang
The phase diagram of hole-doped cuprate superconductors contains three central puzzles: a dome-shaped superconducting phase, a strange metal normal state with Planckian dissipation, and robust d-wave pairing (dx2-y2 symmetry). We propose a unified framework based on a single material-dependent parameter, the coherence purity p, which measures the fraction of phase-coherent condensate relative to dissipative channels. Geometric frustration of the antiferromagnetic background on the CuO2 square lattice drives p to a maximum at optimal doping. The superconducting transition temperature follows T_c proportional to p/(1-p). The d-wave symmetry is derived as the leading pairing instability under on-site repulsion and nearest-neighbor superexchange, without being assumed. In the strange metal, the Planckian dissipation coefficient alpha = hbar/(tau kB T) is linked to the purity deficit 1-p through a universal amplification factor C ≈ 31, which we derive from the nodal Dirac structure of the d-wave state. Fitting the superconducting domes of LSCO and YBCO with the peak purity p_max = 0.97 (fixed from independent transport and high-energy experiments) yields excellent agreement using only two material-dependent scale parameters. The framework produces falsifiable predictions for the doping dependence of the superfluid density and for the product of maximum T_c and the Planckian coefficient. Keywords: high-temperature superconductivity, cuprates, strange metal, Planckian dissipation, d-wave pairing, coherence purity, superconducting dome, LSCO, YBCO
•May 12, 2026•0 citations