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 ${\beta }^{″}\text{−}(\mathrm{BEDT}\text{−}\mathrm{TTF}{)}_2{\mathrm{SF}}_5{\mathrm{CH}}_2{\mathrm{CF}}_2{\mathrm{SO}}_3$. 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.