Weak localization, strong localization, and localization without a metal-insulator transition As I begin to read literature on Anderson localization by disorder, authors are distinguishing between cases that are unfamiliar to me, namely weak localization, strong localization, and localization without a metal-insulator transition.
Can anyone suggest a reference to help me understand the meanings of these terms, and what distinguishes them?
I'm familiar with the simple idea of localized states; states that are confined within a region of space, and of course a metal-insulator transition is when conductivity vanishes on account of the disorder. I can imagine that if localized states have sufficient overlap, a system of localized states could still conduct. Is that an appropriate, if simple, understanding of the transition without localization?
The last point is, what is the difference between weak and strong localization?
 A: I can help to explain the physical meaning of weak localization.
First, there are several characteristic lengthes need to be clarified:

*

*The sample size $L$;

*The mean free path $\ell_{e}$. It is the mean length between two elastic scattering by static centers.

*The phase coherence length $\ell_{\phi}$. It is the distance that electron travels before its phase coherence is destroyed.

Now let's see how the weak localization occurs. If the sample size $L$ is close to $\ell_{\phi}$, and $\ell_{\phi} \gg\ell_{e}$, the total sample is a coherent device, and the electron can maintain its phase coherence even after being scattered for many times. This is the so-called quantum diffusive regime. There are some other regimes but will not be addressed here. The story is that, we can consider two Feynman paths that are time-reversal partners, i.e., one is clockwise and another is anti-clockwise. The interference between those two loops will give a correction to the conductivity, known as the weak localization/anti-localization. If the interference is constructive (such as conventional electron gas), then the electron tends to stay here and the quantum correction to the Drude conductivity is negative; while if the interference is destructive (such as Dirac fermions or spin-orbit coupling induced non-zero Berry phase involved), the quantum correction to the Drude conductivity is positive. The weak loclaization occurs before Anderson localization, or strong localization, where the wavefucntion exponentially decays.
