Spin-density-wave and charge-density-wave fluctuation and electric conductivity

Making use of a microscopic model, we study theoretically the fluctuation contribution to the electric conductivity in the vicinity of the spin-density-wave (SDW) or the charge-density-wave (CDW) transition. We find that the vertex corrections associated with the SDW (or the CDW) fluctuation, which are neglected in earlier works, are of prime importance. For example, we find the excess resistance in the vicinity of the SDW (or the CDW) transition diverges like ‖τ${\mathrm{\Vert }}^{\mathrm{-}\mathrm{\alpha }}$, with α=1/2(4-D) and τ=ln(T/${\mathit{T}}_{\mathit{c}}$), where D is the dimension of the fluctuation in the clean system. This exponent is larger by unity from the value obtained by Horn and Guiddoti [Phys. Rev. B 16, 491 (1977)]. In dirtier samples in which the vertex renormalization is not so important, we recover the result of Horn and Guiddoti. Further, we find a non-Ohmic term in the fluctuation regime. The non-Ohmic conductivity increases with an external electric field ɛ. Moreover, the effect of ɛ is equivalent to the shift in the temperature T by ΔT=-7ζ(3)(ev‖E‖)(4π${\mathit{T}}_{\mathit{c}}$ ${)}^{\mathrm{-}1}$, with ζ(3)=1.202 and v the Fermi velocity in the chain direction. These results account nicely for recent experimental results by Richard et al., which found no explanation until now.