Lamb shift of the Dirac cone of graphene

The fluctuations of the electromagnetic vacuum are one of the most powerful manifestations of the quantum structure of nature. Their effect on the Dirac electrons of graphene is known to induce some spectacular and purely quantistic phenomena, like the Casimir and the Aharanov-Bohm effects. In this work we demonstrate, by using a first-principles approach, that the Dirac cone of graphene is also affected by a sizeable Lamb shift. We show that the microscopic electronic currents flowing on the graphene plane are strongly coupled with the vacuum fluctuations causing a renormalisation of the electronic levels (as large as 4 meV). This shift is one order of magnitude larger than the value predicted for an isolated carbon atom, which imposes a reinterpretation of the Lamb shift as a collective effect.