Revivals of quantum wave-packets in graphene

TL;DR

This paper studies how localized wave-packets in graphene evolve over time under magnetic fields, revealing complex revival phenomena and introducing a new numerical method for solving the Dirac equation with potentials and magnetic fields.

Contribution

It presents a novel numerical scheme for simulating wave-packet dynamics in graphene's Dirac Hamiltonian, highlighting unique revival behaviors and effects of disorder.

Findings

Wave-packets in graphene exhibit rich revival structures.

Disorder influences collapse and revival dynamics.

New numerical method applicable to Dirac equations with potentials.

Abstract

We investigate the propagation of wave-packets on graphene in a perpendicular magnetic field and the appearance of collapses and revivals in the time-evolution of an initially localised wave-packet. The wave-packet evolution in graphene differs drastically from the one in an electron gas and shows a rich revival structure similar to the dynamics of highly excited Rydberg states. We present a novel numerical wave-packet propagation scheme in order to solve the effective single-particle Dirac-Hamiltonian of graphene and show how the collapse and revival dynamics is affected by the presence of disorder. Our effective numerical method is of general interest for the solution of the Dirac equation in the presence of potentials and magnetic fields.