Dimensional Crossover of Weak Localization in a Magnetic Field

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.Comment: RevTeX, 11 pages, 4 figures; three references added and discusse

Additional file 1: of The effects of facemasks on airway inflammation and endothelial dysfunction in healthy young adults: a double-blind, randomized, controlled crossover study

Table S1. Filtration Efficiencies and resistance of six types of facemasks. (DOCX 36 kb