Weak localization: Quantitative treatment

(2) Dimensionality: Generally speaking, in any particular WL problem there will be 2 char. lengths: (i) the elastic mfp, l, which is usually only weakly T -dependent and can range, typically, from a few Å to a few 1000 Å (ii) some ”phase-breaking length Lφ, e.g., an inelastic length Lin or a “magnetic length” LM ∼ √ φ0/B. The phasebreaking length can be l. Most experiments which explicitly test theory of WL done on thin wires or films, such that the “small” dimension d is phase-breaking length Lφ but usually l; however, in the case of (e.g.) Si MOSFET’s, clearly d l. I will go through the theory explicitly for the former case, so that “locally” (on the scale of l) the system looks 3D; the generalization to the case of a “locally 2D” (or 1D) system is straightforward and mainly affects the dimensional and numerical factors.