# Weak Anti-Localization

On Wikipedia (pretty much the only place I can find an explanation of what weak anti-localization actually is) it is explained as:

In a system with spin-orbit coupling the spin of a carrier is coupled to its momentum. The spin of the carrier rotates as it goes around a self-intersecting path, and the direction of this rotation is opposite for the two directions about the loop. Because of this, the two paths any loop interfere destructively which leads to a lower net resistivity.

The last bit is the part I don't get, I would have thought that if the two paths interfere destructively then surely the resistivity would increase? What does the spin-orbit coupling change, since that seems to be the only difference between antilocalization and localization which seem to result in two opposite effects on the resistivity.

My understanding is that for weak localization the presence of weak disorder leads to some electron paths interfering destructively since there is an equal probability for it to take one complete "circle" in one direction to taking the same path in the opposite direction so the phases cancel, resulting in fewer electrons diffusing all the way through the material and hence we would measure an increase in resistivity. Is this correct?

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The paths which interfere are in facts paths which return to the origin (there is no interference for the paths transversing the sample). In the conventional weak localisation, the paths interfere constructively which leads to an increased probability of reflection and thus to an increase in resistance. For weak anti-localization, everything goes the other way around.

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Okay I think I see where I went wrong. With weak localization, the back scattering is enhanced due to the constructive interference of the paths around the closed loop. With weak anti-localization because the spin is related to the momentum which depends on the path then the "forward" and "backward" paths interfere destructively so there is a lower amplitude on the backscattering paths, hence electrons are more likely to travel through the medium and resistivity decreases? –  Josh Sep 28 '12 at 15:17
@josh: exactly... for more information, see e.g. Mesoscopic Physics of Electrons and Photons by Eric Akkermans and Gilles Montambaux. –  Fabian Sep 28 '12 at 16:03