Drude weight and optical conductivity of doped antiferromagnets.

Abstract

The optical conductivity is calculated within the t-J model for low hole-dopant concentrations. The calculations are done on the basis of a Green's-function formalism within a slave-fermion Schwinger-boson representation. The Green's function for holes is calculated in the self-consistent Born approximation to first order in the dopant concentration \ensuremath{\delta}. The Drude weight D is determined by applying a gauge-invariance condition and Ward's identity. It is found that D is proportional to \ensuremath{\delta} and the inverse effective mass of quasiparticles in the hole pockets. It increases gradually with increasing ratio J/t. We compare our results with those of exact diagonalizations. The latter are obtained for larger values of \ensuremath{\delta} only and therefore must be extrapolated to low dopant concentrations. The two results differ and we argue that nonlinear \ensuremath{\delta} dependences of D appear already at rather low \ensuremath{\delta} values. The finite-frequency conductivity is also calculated by taking account of the lowest-order diagrams for the Green's function of the current. Like previous results for exact diagonalizations of small clusters, large weight is found in the vicinity of the frequencies characteristic of spin excitation. It may be associated with the midinfrared band observed in experiments.