Comparison of coherent and weakly incoherent transport models for the interlayer magnetoresistance of layered Fermi liquids

Abstract

The interlayer magnetoresistance of layered metals in a tilted magnetic field is calculated for two distinct models for the interlayer transport. The first model involves coherent interlayer transport, and makes use of results of semiclassical or Bloch-Boltzmann transport theory. The second model involves weakly incoherent interlayer transport where the electron is scattered many times within a layer before tunneling into the next layer. The results are relevant to the interpretation of experiments on angular-dependent magnetoresistance oscillations ͑AMRO͒ in quasi-one-and quasi-two-dimensional organic metals. We find that the dependence of the magnetoresistance on the direction of the magnetic field is identical for both models except when the field is almost parallel to the layers. An important implication of this result is that a three-dimensional Fermi surface is not necessary for the observation of the Yamaji and Danner oscillations seen in quasi-two-and quasi-onedimensional metals, respectively. A universal expression is given for the dependence of the resistance at AMRO maxima and minima on the magnetic field and scattering time ͑and thus the temperature͒. We point out three distinctive features of coherent interlayer transport: ͑i͒ a beat frequency in the magnetic oscillations of quasi-two-dimensional systems, ͑ii͒ a peak in the angular-dependent magnetoresistance when the field is sufficiently large and parallel to the layers, and ͑iii͒ a crossover from a linear to a quadratic field dependence for the magnetoresistance when the field is parallel to the layers. Properties ͑i͒ and ͑ii͒ are compared with published experimental data for a range of quasi-two-dimensional organic metals. ͓S0163-1829͑99͒02236-5͔

Cyclotron effective masses in layered metals

“…For typical organic metals this ratio is less than 0.01. 3,8 Taking the derivative of Eq. ͑6͒ with respect to ⑀ F gives, for the cyclotron mass,…”

Absence of metal–insulator transition and coherent interlayer transport in oriented graphite in parallel magnetic fields

“…Coherent transport means therefore that band states extend over many layers and a 3D Fermi surface can be defined. In the other case, incoherent transport is diffusive and neither a 3D Fermi surface nor the Bloch-Boltzmann transport theory is applicable [24]. In order to check this and the role played by disorder we have performed measurements of the out-of-plane electrical resistivities with high angle resolution.…”

Interplay between angular and quantum magnetoresistance oscillations

“…(2) was confirmed in Ref. [5] with the help of Kubo formula in the twolayer model in the limit Γ 0 t z (Γ 0 =h/(2τ 0 ) is the electron-level width due to scattering on impurities in zero-magnetic field), where electrons on average scatter on impurities many times before tunneling on the adjacent conducting layer. Therefore, this limit was called "weakly incoherent" in Ref.…”

“…Therefore, this limit was called "weakly incoherent" in Ref. [5]. However, since the obtained formulas for conductivity turned out to be the same as in the coherent limit, in Ref.…”

“…Since Eq. (2) was obtained within the framework of the approximate model, namely, in the τ -approximation [3] or neglecting the MQO [5], in our calculations we use a more rigorous two-layer model that takes into account MQO in the limit t z √h ω c Γ 0 .…”