Conductivity of 1D electrons in anisotropic 3D medium

Abstract

Discusses the phonon limited high-temperature conductivity of 1D electrons within the quasistatic limit for lattice vibrations ( omega tau <<1 where omega is the phonon frequency and tau is the electron scattering time) using both first and second Born approximations and electron-one-phonon interaction. The second-order contribution of acoustic phonons to tau -1 is shown to be divergent when the phonons are 1D as well. This divergence indicates that the second-order contribution to the resistivity may be important in the case of anisotropic 3D acoustic phonons. The authors show that the ratio between the first- and second-order electron scattering rates is: tau 2-1/ tau 1-1 varies as ( lambda / alpha )(T/ epsilon F); where lambda is the dimensionless /electron-phonon coupling constant and alpha =vperpendicular to /v/sub /// is the ratio of the sound velocities perpendicular to and along the chain direction. Thus the second-order contribution is seen to be enhanced for small alpha . The theory is applied to the resistivity of mercury chains in Hg3- delta AsF6 where alpha is known to be very small. It is compared with previous experimental results of rho (T) as well as with a newly obtained one at an extended temperature region, up to 430K. It is shown that the expression for the resistivity which follows from the authors' theory; rho =AT+BT2 can account for the experimental data in the temperature range 235K-430K. The electron-multiphonon series in first Born approximation for atomic chains is summed in the quasi-static limit and is shown to be strongly suppressed. The organic conductor TTF-TCNQ is also discussed. Here the present-second order contribution is shown to be smaller because the phonons are isotropic ( alpha approximately=1).