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

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.