Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory

TL;DR

This paper develops an analytic semiclassical method to compute electron-hole pair production in biased bilayer graphene under electric fields, revealing new wavefunction features and establishing the tunnelling current's normalization.

Contribution

It introduces a fully analytic semiclassical approach using analytic continuation, improving understanding of pair production in bilayer graphene beyond numerical methods.

Findings

Derived an analytic expression for pair production rate

Identified non-standard wavefunction features in biased bilayer graphene

Established the normalization of the tunnelling current

Abstract

Employing a semiclassical method based on analytic continuation, we compute the electron-hole pair production rate in biased bilayer graphene subject to an in-plane electric field. This approach, originally due to Zwaan, bypasses the need for exact solutions at turning points, which are generally unavailable beyond linear or quadratic band structures. Applying this technique to biased bilayer graphene reveals non-standard features of the asymptotic wavefunctions, in particular the necessity of retaining decaying components even in classically allowed regions. By providing a fully analytic solution, this work complements and clarifies earlier results based on hybrid analytical-numerical treatments, and importantly establishes the absolute normalisation of the pair production rate -- and hence of the tunnelling current.