Dimensional Crossover of Weak Localization in a Magnetic Field

TL;DR

This paper investigates how weak localization transitions from three-dimensional to lower-dimensional behavior in anisotropic systems due to temperature and magnetic field effects, revealing persistent localization effects even at high magnetic fields.

Contribution

It introduces a detailed analysis of the dimensional crossover of weak localization in anisotropic lattices under magnetic fields, including the role of diffusion coefficients and magnetic length.

Findings

Dimensional crossover occurs when phase coherence length or magnetic length becomes comparable to lattice spacing.

Weak localization persists even at large magnetic fields in lattice systems.

The magnetic field orientation influences the crossover behavior and localization effects.

Abstract

We study the dimensional crossover of weak localization in strongly anisotropic systems. This crossover from three-dimensional behavior to an effective lower dimensional system is triggered by increasing temperature if the phase coherence length gets shorter than the lattice spacing $a$. A similar effect occurs in a magnetic field if the magnetic length $L_m$ becomes shorter than $a(D_{||}/D_\perp)^\gamma$, where $\D_{||}/D_\perp$ is the ratio of the diffusion coefficients parallel and perpendicular to the planes or chains. $\gamma$ depends on the direction of the magnetic field, e.g. $\gamma=1/4$ or 1/2 for a magnetic field parallel or perpendicular to the planes in a quasi two-dimensional system. We show that even in the limit of large magnetic field, weak localization is not fully suppressed in a lattice system. Experimental implications are discussed in detail.