Effects of discrete topology on quantum transport across a graphene $n-p-n$ junction: A quantum gravity analogue

TL;DR

This paper explores how the discrete topology of a graphene lattice influences quantum transport in $n-p-n$ junctions, proposing an experiment to simulate quantum gravity effects through measurable transmittance changes.

Contribution

It introduces an effective quantum dynamics framework incorporating next-to-nearest atom hopping, revealing the impact of lattice discreteness on Klein tunnelling and proposing an experimental simulation of quantum gravity.

Findings

Discrete topology affects Klein tunnelling in graphene.

The effective Dirac structure is not chirally symmetric.

Proposed experiment to measure transmittance for quantum gravity analogues.

Abstract

In this article, we investigate the effect of next-to-the-nearest atom hopping on Klein tunnelling in graphene. An effective quantum dynamics equation is obtained based on an emergent generalized Dirac structure by analyzing the tight-binding model beyond the linear regime. We show that this structure has some interesting theoretical properties. First, it can be used to simplify quantum transport calculations used to characterize Klein tunnelling; second, it is not Chirally symmetric as hinted by previous work. Finally, it is reminiscent of theories on a space with a discrete topology. Exploiting these properties, we show that the discrete topology of the crystal lattice has an effect on the Klein tunnelling, which can be experimentally probed by measuring the transmittance through $n-p-n$ junctions. We argue that this simulates quantum gravitational analogues using graphene and we propose an experiment to perform such measurements.