\hot Spots" in Quasi-one-dimensional Organic Conductors

The distribution of the electron scattering rate on the Fermi surface of a quasi-one-dimensional conductor is calculated for the electron-electron umklapp interaction. We nd that in certain regions on the Fermi surface the scattering rate is anomalously high. The reason for the existence of these \hot spots" is analogous to the appearance of the van Hove singularities in the density of states. We employ a generalized-approximation (where the scattering integral in the Boltzmann equation is replaced by the scattering time which depends on the position at the Fermi surface) to study the dependence of the electric resistance on the amplitude and the orientation of a magnetic eld. We nd that the \hot spots" do not produce a considerable magnetoresistance or commensurability eeects at the \magic angles". In a recent paper 1], Chaikin suggested phenomeno-logically that \hot spots", the regions where the electron scattering rate is anomalously high, may be present at the Fermi surface (FS) of the (TMTSF)2X organic metals. With a particular choice of the model parameters, he was able to explain the experimental data 2] on the angular dependence of magnetoresistance (the Lebed's \magic angles" effect 3]). However, the microscopic origin of the \hot spots" was not speciied in Ref. 1]. In an earlier paper 4], it was mentioned that the electron-electron umklapp scattering or the scattering on a soft phonon mode in the vicinity of a charge/spin-density-wave transition may lead to formation of the \hot spots". The latter idea was elaborated in detail in Ref. 5]. In the present paper, we calculate straightforwardly the distribution of the electron scattering rate on the Fermi surface (FS) of a quasi-one-dimensional (Q1D) conductor due to the electron-electron umklapp scattering and demonstrate that the \hot spots" indeed exist. Let us consider a Q1D metal which consist of parallel conducting chains. The axis x is in the direction of the highest conductivity (along the chains), the axes y (also referred to as b) and z (or c) are in the directions of the lower and the lowest conductivities, and both directions are perpendicular to the chains. The Fermi momentum in the x-direction is equal to kF ((h = 1). In the umklapp scattering process, the total momentum of the two scattering electrons changes by the value 4kF which is equal to the lattice wave vector in the (TMTSF)2X compounds. The scattering rate (the inverse of the lifetime) of the electron with the …