Topological Gauge Structure and Phase Diagram for Weakly Doped Antiferromagnets

We show that a topological gauge structure in an effective description of the $t\mathrm{\text{−}}J$ model gives rise to a global phase diagram of antiferromagnetic and superconducting phases in a weakly doped regime. Dual confinement and deconfinement of holons and spinons play essential roles here, with a quantum critical point at a doping concentration $x_c\simeq 0.043$. The complex experimental phase diagram at low doping is well described within such a framework.

Figure 1

In the spinon Bose condensed phase, a holon-meron is confined with an antimeron to form a hole-dipole composite, which carries a charge $+\mathrm{e}$ and spin $1/2$. The arrows denote ${\mathbf{n}}_i\propto \mathbf{(}\mathbf{-}1{\mathbf{)}}^i⟨{\mathbf{S}}_i⟩$.

Figure 2

Phase diagram at low doping $x$: A dual confinement-deconfinement occurs at a quantum critical point $x_c\simeq 0.043$. The Néel temperature $T_N$ vanishes at $x_0\simeq 0.03$. $T_f$ and $T_g$ denote characteristic spin freezing temperatures, and $T_c$ is the superconducting transition temperature. $E_g$ is a characteristic spin energy (see text).