# Spin trumps pseudospin in a Dirac antiperovskite

Measurements of weak antilocalization in Sr_{3}SnO reveal a "hidden" spin-momentum entanglement.

Quantum mechanics blurs the distinction between particles and waves. A rather exotic manifestation of the wavelike nature of electrons in solids, revealed by a simple measurement of electrical resistance, is weak localization. The probability of an electron propagating from points A to B is determined by summing the complex quantum-mechanical amplitude of every possible path. When points A and B are identical (closed loop), the probability is enhanced due to constructive interference between clockwise and counterclockwise paths that always return with matching phases. Hence, there is an extra probability for an electron to remain in its position (i.e., localized), resulting in a positive correction to the resistivity at low temperatures and zero magnetic field (weak localization).

The opposite is also possible: in some solids, a phase shift could occur between the two time-reversed paths, resulting in weak *anti*localization. Traditionally, antilocalization has been attributed to the spin-orbit coupling in a material, but this is sometimes misleading. An interesting recent example is graphene, where electrons acquire such a phase shift by going around one of the Dirac points in momentum (*k*) space. This extra phase, which the electrons obtain by encircling a singular point in *k*-space, comes from *pseudo*spin, and gives rise to destructive interference for closed-loop paths. An open question is what happens in a solid where both real spin and pseudospin are at play. In the case of graphene, the spin-orbit coupling of the light carbon atoms is too small, so pseudospin trumps real spin in the generation of weak antilocalization.

Nakamura *et al*. observed signatures of weak antilocalization in thin films of Sr_{3}SnO grown by molecular beam epitaxy (MBE). By fitting the data to a *three-dimensional* (anti)localization model newly developed by colleagues in the Quantum Many-Body Theory Department, the authors found that intervalley scattering suppresses the role of pseudospin in generating weak antilocalization. Instead, the weak antilocalization arises from a “hidden” entanglement of real spin with momentum.

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