Tunnelling through finite graphene superlattices: resonance splitting effect

TL;DR

This paper derives an exact formula for electron transmission through finite graphene superlattices, revealing resonance splitting phenomena that depend on the number of barriers, applicable to various potential types and shapes.

Contribution

It provides a novel analytical expression for transmission probability in finite graphene superlattices with arbitrary barriers, highlighting resonance splitting effects.

Findings

Resonance energies split into multiple peaks as barriers increase.

The derived formula applies to both electric and magnetic potentials.

Numerical results confirm the analytical predictions across different superlattice configurations.

Abstract

An exact expression of the transmission probability through a finite graphene superlattice with an arbitrary number of potential barriers $n$ is derived in two cases of the periodic potential: rectangular electric potential and $\delta$-function magnetic potential. Obtained transmission probabilities show two types of resonance energy: barrier-induced resonance energies unchanged as $n$ varies and well-induced resonance energies undergone the $(n - 1)$-fold splitting as $n$ increases. Supported by numerical calculations for various types of graphene superlattices, these analytical findings are assumed to be in equal applied to all of finite graphene superlattices regardless of potential natures [electric or magnetic] as well as potential barrier shapes.