Comment on "Magnetic quantum oscillations of the conductivity in layered   conductors"
  We discuss the recent theory of Gvozdikov [Phys. Rev. B 70, 085113 (2004)] which aims at explaining the Shubnikov-de Haas oscillations of the longitudinal resistivity \rho_zz observed in the quasi-two-dimensional organic compound \beta''-(BEDT-TTF)_2SF_5CH_2CF_2SO_3.   We point out that the self-consistent equations of the theory yielding the longitudinal resistivity and the magnetic field dependence of the chemical potential have been incorrectly solved. We show that the consideration of the self-consistent Born approximation (which determines the relaxation rate in Gvozdikov's paper) leads in fact to the complete absence of the longitudinal conductivity \sigma_{zz} at leading order in high magnetic fields. 
T. Champel and V.P. Mineev