Intrinsic phase fluctuations and superfluid density in doped Mott insulators

The doping dependence of the superfluid density ${\ensuremath{\rho}}_{\text{s}}$ exhibits distinct behaviors in the underdoping and overdoping regimes of cuprates, while the superconducting (SC) transition temperature ${T}_{c}$ generally scales with ${\ensuremath{\rho}}_{\text{s}}$. In this paper, we present a unified understanding of the superconducting transition temperature ${T}_{c}$ and ${\ensuremath{\rho}}_{\text{s}}$ across the entire doping range by incorporating the underlying mutual Chern-Simons gauge structure that couples the spin and charge degrees of freedom in a doped Mott insulator. Within this framework, the SC phase fluctuations are deeply intertwined with the spin dynamics, such that thermally excited neutral spins determine ${T}_{c}$, while quantum spin excitations effectively reduce the superfluid density at zero temperature. As a result, a Uemura-like scaling of ${T}_{c}$ vs ${\ensuremath{\rho}}_{\text{s}}$ in the underdoped regime naturally emerges, while the suppression of both ${T}_{c}$ and ${\ensuremath{\rho}}_{\text{s}}$ at overdoping is attributed to a drastic reduction of antiferromagnetic spin correlations.