Incoherence, metal-to-insulator transition, and magnetic quantum oscillations of interlayer resistance in an organic conductor

An analytic theory is developed for the conductivity across the layers σzz in a layered conductor in perpendicular magnetic field under the conditions of interlayer incoherence. The latter assumes a small hopping integral between the layers t⪡∕τ and the presence of localized states in the tails of broadened Landau levels (LLs) (τ is the electron scattering time within the layers). In the incoherent regime, σzz strongly depends on the in-plane conductivity mechanisms because electrons spend most of their time within the weakly coupled layers. At high fields Ωτ⪢1, an integer quantum Hall effect (IQHE) within the layers develops which changes dramatically magnetic quantum oscillations in the σzz compared to the standard Lifshitz-Kosevich theory (Ω is the cyclotron frequency). At low fields, σzz displays Shubnikov--de Haas (SdH) oscillations which in the limit Ωτ⪢1 transforms into sharp peaks. The peaks reach their maximum values σzz∝ΩT when LLs cross the chemical potential μ. When μ falls into the tails between the LLs, the σzz displays first a thermal activation behavior σzz∝exp[-(Ω-μ)∕T] and, then at lower temperatures T, crosses over into a variable-range-hopping regime with σzz∝exp(-√T₀∕T), where T₀∝B-B₀^γ. Above B₀, the in-plane electrons are in the quantum-Hall-insulator regime and the background interlayer magnetoresistance Rb has an insulatorlike temperature dependence. Below B₀, the in-plane electrons are in the conventional SdH oscillation regime and Rb has a metal-like temperature dependence. On the insulating side, Rb displays a universal dependence on the scaling variable (B-B₀)∕T^κ. Scaling is destroyed in tilted magnetic fields at angles corresponding to the spin zeros. All the above features in the σzz have been observed in the ${{β}}^{{''}}{{-}}{(BEDT{{-}}TTF)}₂S{F}₅C{H}₂C{F}₂S{O}₃$, in which the critical exponent is equal to ${κ}=1∕{γ}=0.65$. The IQHE regime at high fields in this quasi-two-dimensional organic conductor is favored by the fixed value of the chemical potential. It is shown that at low temperatures $(T⪡{}∕{τ})$, oscillations of the conductivity and magnetization are related by the condition ${{σ}}zz{∝}{B}²{∂}{ ̃ \~{}{}}{M}∕{∂}B$, in agreement with observations in ${{β}}^{{''}}{{-}}{(BEDT{{-}}TTF)}₂S{F}₅C{H}₂C{F}₂S{O}₃$. The analysis shows that the above features in the conductivity cannot be explained within the model with a narrow-band dispersive electron transport across the layers because the model is incompatible with the incoherence condition t⪡∕τ. Moreover, in the self-consistent Born approximation, this model yields a nonphysical negative conductivity σzz<0.