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A Zener diode is a paradigmatic device in semiconductor-based electronicsthat consists of a pn junction where an external electric field induces aswitching behavior in the current-voltage characteristics. We study Zenertunneling in HgTe quantum wells and graphene multilayers. We find that thetunneling transition probability depends asymmetrically on the parallelmomentum of the carriers to the barrier. In HgTe quantum wells the asymmetry isthe opposite for each spin, whereas for graphene multilayers it is the oppositefor each valley degree of freedom. In both cases, a spin/valley current flowingin the perpendicular direction to the applied field is produced. We relate theorigin of this Zener tunneling spin/valley Hall effect to the Berry phaseacquired by the carriers when they are adiabatically reflected from the gappedregion.

Zener tunneling isospin Hall effect in HgTe quantum wells and graphene multilayers