Magnetic Quantum Oscillations of the Longitudinal Conductivity $σ_{zz}$ in Quasi two-dimensional Metals

Abstract

We derive an analytical expression for the longitudinal magnetoconductivity $σ_{zz}$ in layered conductors in presence of a quantizing magnetic field perpendicular to the layers and for short-range in-plane impurity scattering in frame of the quantum transport theory. Our derivation points out quite unusual temperature and magnetic field dependences for Shubnikov-de Haas oscillations in the two-dimensional limit, i.e. $\hbar ω_{c} \gg 4 πt$, where $t$ is the interlayer hopping integral for electrons, and $ω_{c}$ the cyclotron frequency. In particular, when $\hbar ω_{c} \gg 4 πt$ and $\hbar ω_{c} \geq 2 πΓ_μ$ (here $Γ_μ$ is the value of the imaginary part of the impurity self-energy at the chemical potential $μ$), a pseudo-gap centered on integer values of $μ/\hbarω_{c}$ appears in the zero-temperature magnetoconductivity function $σ_{zz}(μ/\hbarω_{c})$. At low temperatures, this high-field regime is characterized by a thermally activated behavior of the conductivity minima (when chemical potential $μ$ lies between Landau levels) in correspondence with the recent observation in the organic conductor $β''\text{-(BEDT-TTF)}_{2}\text{SF}_{5}\text{CH}_{2}\text{CF}_{2}\text{SO}_ {3}$.