Emergent Pair Density Wave and Incoherent Metallic State in a Strongly Correlated Doped System

Abstract

We investigate the dynamical emergence of a state driven by the interplay between antiferromagnetism (AFM) and singlet $d$-wave superconductivity (SC) within a slave-rotor mean-field framework. By decomposing the electron into charge and spin degrees of freedom, the formalism captures strong-correlation effects beyond conventional mean-field approaches. A PDW order is found to emerge dynamically in the coexistence region of AFM and SC. The AFM-SC coexistence region is significantly modified with correlation, leading to a systematic shift of the tetra-critical point. The doping and temperature evolution of the AFM, SC, and PDW order parameters, together with the rotor condensate amplitude $ϕ$, which characterizes charge coherence, shows a crossover from a coherent to an incoherent metal with the suppression of coherent quasi-particle spectral weight. Moreover, in the AFM + $(ϕ\neq 0)$ region, coherent quasi-particle bands coexist with incoherent Hubbard-like excitations, whereas only incoherent spectral features survive in the AFM + $(ϕ= 0)$ regime. The SC phase exhibits nodal quasi-particles consistent with $d$-wave pairing.