On galvanomagnetic effects in layered conductors

In the quasidassical approximation we analyze the dependences of the resistivity p and Hall field on the magnetic field orientation and intensity in layered conductors with quasi-» energy spectrum of arbitrary form~ The Shubnikov-de Haas amplitudes are shown to drop abruptly and the smooth part of magnetoresistance to increase at certain orientation of H when the respective extreme (Fermi surface) FS cross section is self-intersectingAnisotropy of p, depending essentially on FS topology, manifests itself most when the current flows across the layers. In recent years, interest in physical properties of layer conductors has grown considerably. A wide class of superconductors NbSe2, lbS2 dichalcogenides of transition metals, cuprate based metal oxide compounds, organic conductors such as salts of tetrathiafulvalen ~BEDTTTF~, halogens of tetraseleniumtetracen ~TSeT), etc. represents layered structures with a sharp anisctropy of electrical conductivity in the normal (non-superconducting) states. They have an anomalously low electrical conductivity along the n direction normal to a certain plane. The experimentally observed Shubnikov-de Haas oscillation of ma gnetoresistance in organic conductors (see, for example [1-10] and Refs, there in) and metal type of electrical conductivity in most of them make it quite reasonable to believe that the well founded concept of charge carriers in metals is also applicable for describing electron properties of the layered conductors. Nevertheless the only way to prove the correctness of using the concept of elementary excitations, similar to conduction electrons in metals, is the solution of the inverse problem of reconstructing the Fermi surface (FS) from experimental data, ln particularly, topology of FS, can be reliably determined by studying galvanomagnetic phenomena [I ii. lUet us consider a conductor with quasi-two dimensional electron energy spectrum, placed in d,c, uniform magnetic field II. A small curvature in the direction normal to layers is characteristic of all FS geometries of sharply anisotropic conductors. Therefore it is quite justified to make use in this case of the strong coupling approximation, It means that a coefficient An in the expression (° l+esent address: High school in Sokode, Togo. 1470 JOURNAL DE PHYSIQUE I N°10 for the energy of charge carriers £(P) = i~ An (Pz, Pv) CDS (nPz/hq) (1) can be assumed to be rapidly decreasing with n and all An at n > I to be much less than Fermi energy SF. Here h is the Planck's constan~ q = ja x bjla(b x c), (2) and a, b, c the basic vectors of the single crystal, forming the primitive elementary cell, with a and b lying in the layer plane (z, y). A weak dependence of the energy on the electron momentum projection pz is due to the slow charge carriers motion across the layers. The velocity of this motion Vz " °£/°Pz " j§(~/h~) An (Pz Py) ~'~ (~Pz /hg) (3) b considerably smaller than the maximum drift velocity vF of charge carriers in the layer plane. The condition v~"" = vo = QVF < vF (4) will be assumed below to be arrays satisfied. The isoenergetic surface s(p) = s, depending on the type of the function Ao (Pz> Py) can be either a system of weakly corrugated cylinders (isolated or interconnected by thin links), or elongated closed surfaces in the momentum space, when s is near to the energy band boundaries. lb determine the electric current density 11 = / d~P2evif(P)/(2~h)~ = «;>E> (5) it is necessary to solve the BoltzJnann equation for the distribution function of charge carders f(p) = fo(s) eE# 3 folds, which within a linear approximation ~vith respect to weak electrical field E and T approximation of collision integral fi'( f) = f fo) /r has a rather sbnple form o~/ot + ~/r = v. (6)