Common path interference in Zener tunneling is a universal phenomenon

TL;DR

This paper demonstrates that Zener tunneling probability exhibits universal oscillations due to common path interference, arising from higher order dispersion terms, and is observable in materials like bilayer graphene.

Contribution

It reveals the universal occurrence of oscillatory Zener tunneling caused by common path interference, linked to higher order dispersion terms in the energy relation.

Findings

Zener tunneling probability is non-monotonic and oscillatory.

Oscillations are caused by interference between two tunneling solutions.

Bilayer graphene is an ideal candidate for observing this phenomenon.

Abstract

We show that the probability of electric field induced interband tunneling in solid state systems is generically a non-monotonic (oscillatory) function of the applied field. This unexpected behavior can be understood as arising due to a common path interference between two distinct tunneling solutions. The phenomenon is insensitive to magnetic field, and arises whenever the low energy dispersion relation contains higher order terms in addition to the usual $p^2$ term. Such higher order terms are generically present, albeit with small co-efficient, so that the oscillatory Zener tunneling is a universal phenomenon. However, the first `Zener oscillation' occurs at a transmission probability which is exponentially small when the co-efficient of the higher order terms is small. This explains why this oscillatory aspect of Zener tunneling has been hitherto overlooked, despite its universality. The common path interference is also destroyed by the presence of odd powers of $p$ in the low energy dispersion relation. Since odd powers of $p$ are strictly absent only when the tunneling barrier lies along an axis of mirror symmetry, it follows that the robustness of the oscillatory behavior depends on the orientation of the tunneling barrier. Bilayer graphene is identified as a particularly good material for observation of common path interference, due to its unusual nearly isotropic dispersion relation, where the $p^4$ term makes the leading contribution.