Lamb shift of the Dirac cone of graphene

Pedro Melo, Andrea Marini

Published 2016-05-30Version 1

The fluctuations of the electromagnetic vacuum are one of the most powerful manifestations of the quantum structure of nature. Those fluctuations are connected to the quantization of the electromagnetic field, whose interaction with the Dirac electrons of graphene is known to induce some spectacular and purely quantistic phenomena, like the Casimir and the Aharanov--Bohm effects. This interaction is also responsible for the shift of the electronic levels, well known as the electronic Lamb shift. In this work we demonstrate, by using a first principles approach, that the Dirac cone of graphene is affected by a seizable Lamb shift of the electronic levels (as large as 4 meV) and of the velocities. This Lamb shift is one order of magnitude larger than the value predicted for an isolated carbon atom. This confirms the unique interaction of the massless electrons of graphene with the electromagnetic vacuum oscillations. We also give a sound interpretation of this Lamb shift in terms of a collective phenomena and trace it back to the interaction of the quantized vector potential with the microscopic electronic currents flowing on the graphene plane.