Phenomenology of Conduction in Incoherent Layered Crystals

TL;DR

This paper introduces a phenomenological model linking resistive anisotropy to phase coherence lengths in incoherent layered crystals, analyzing conduction behavior and magnetoresistivity with temperature-dependent coherence lengths.

Contribution

It presents a new phenomenological approach connecting resistive anisotropy to phase coherence lengths, including model-independent implications and effects of temperature variations.

Findings

Resistive anisotropy relates to phase coherence lengths.

Out-of-plane coherence length is approximately fixed at interlayer spacing.

Conduction regimes vary with temperature and coherence length changes.

Abstract

A novel phenomenological approach to the analysis of the conductivities of incoherent layered crystals is presented. It is based on the fundamental relationship between the resistive anisotropy $\sigma_{ab}/\sigma_c$ and the ratio of the phase coherence lengths in the respective directions. We explore the model-independent consequences of a general assumption that the out-of-plane phase coherence length of single electrons is a short fixed distance of the order of interlayer spacing. Several topics are discussed: application of the scaling theory, magnetoresistivity, the effects of substitutions and the intermediate regime of conduction when both coherence lengths change with temperature, but at different rate.