An understanding of the anomalous charge dynamics in the high-$T_c$ cuprates is obtained based on a model study of doped Mott insulators. The high-temperature optical conductivity is found to generally have a two-component structure: a Drude-like part followed by a mid-infrared band. The scattering rate associated with the Drude part exhibits a linear-temperature dependence over a wide range of high temperature, while the Drude term gets progressively suppressed below a characteristic energy of magnetic origin as the system enters the pseudogap phase. The high-energy optical conductivity shows a resonancelike feature in an underdoped case and continuously evolves into a $1∕\omega$ tail at higher doping, indicating that they share the same physical origin. In particular, such a high-energy component is closely correlated with the $\omega$-peak structure of the density-density correlation function at different momenta, in systematic consistency with exact diagonalization results based on the $t\text{−}J$ model. The underlying physics is attributed to the high-energy spin-charge separation in the model, in which the “mode coupling” responsible for the anomalous charge properties is not between the electrons and some collective mode but rather between charge carriers, holons, and a topological gauge field controlled by spin dynamics, as the consequence of the strong short-range electron-electron Coulomb repulsion in the doped Mott insulator.

• Received 7 January 2007

DOI:https://doi.org/10.1103/PhysRevB.76.024501