Electronic Branched Flow in Graphene with Random Potential: Theory and Machine Learning Prediction

Research paper by Marios Mattheakis, G. P. Tsironis, Efthimios Kaxiras

Indexed on: 24 Jan '18Published on: 24 Jan '18Published in: arXiv - Physics - Mesoscopic Systems and Quantum Hall Effect


We investigate the ultra-relativistic electronic flow in a two-dimensional random potential relevant to charge carrier dynamics in Dirac solids. As an example, the random potential in graphene, the prototypical Dirac solid, arises from inhomogeneous charge impurities in the substrate, a common feature in experimental systems. An additional bias voltage is introduce to tune the electronic propagation. We show that the onset of {electronic branched flow} is determined by the statistical properties of the potential and we provide a scaling-type relationship that describes the emergence of branches. We also show that, despite the statistical nature of branching, reservoir computing provides an accurate detection mechanism for the caustics. The onset of branching is predicted through a deep learning {algorithm}, which may be implemented experimentally to improve materials properties of graphene substrates.