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 sigma(zz) 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 << h/tau and the presence of localized states in the tails of broadened Landau levels (LLs) (tau is the electron scattering time within the layers). In the incoherent regime, sigma(zz) strongly depends on the in-plane conductivity mechanisms because electrons spend most of their time within the weakly coupled layers. At high fields Omega tau >> 1, an integer quantum Hall effect (IQHE) within the layers develops which changes dramatically magnetic quantum oscillations in the sigma(zz) compared to the standard Lifshitz-Kosevich theory (Omega is the cyclotron frequency). At low fields, sigma(zz) displays Shubnikov-de Haas (SdH) oscillations which in the limit Omega tau >> 1 transforms into sharp peaks. The peaks reach their maximum values sigma(zz)proportional to h Omega/T when LLs cross the chemical potential mu. When mu falls into the tails between the LLs, the sigma(zz) displays first a thermal activation behavior sigma(zz)proportional to exp [-(h Omega-mu)/T] and, then at lower temperatures T, crosses over into a variable-range-hopping regime with sigma(zz)proportional to-exp(-root T-0/T), where T-0 proportional to parallel to B-B-0 parallel to(gamma). Above B-0, the in-plane electrons are in the quantum-Hall-insulator regime and the background interlayer magnetoresistance R-b has an insulatorlike temperature dependence. Below B-0, the in-plane electrons are in the conventional SdH oscillation regime and R-b has a metal-like temperature dependence. On the insulating side, R-b displays a universal dependence on the scaling variable (B-B-0)/T-kappa. Scaling is destroyed in tilted magnetic fields at angles corresponding to the spin zeros. All the above features in the sigma(zz) have been observed in the beta"-(BEDT-TTF)(2)SF5CH2CF2SO3, in which the critical exponent is equal to kappa=1/gamma=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 << h/tau), oscillations of the conductivity and magnetization are related by the condition sigma(zz)proportional to B-2 partial derivative(M) over bar/partial derivative B, in agreement with observations in beta"-(BEDT-TTF)(2)SF5CH2CF2SO3. 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 << h/tau. Moreover, in the self-consistent Born approximation, this model yields a nonphysical negative conductivity sigma(zz)< 0.