Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene

TL;DR

This paper demonstrates that Coulombic quantum fluctuations lift the orbital degeneracy of zero-energy Landau levels in bilayer graphene, leading to a Lamb-shift-like splitting and complex evolution of pseudo-zero-mode levels.

Contribution

It reveals a quantum effect analogous to the Lamb shift in bilayer graphene, showing how Coulomb interactions lift degeneracies in Landau levels.

Findings

Orbital degeneracy is lifted by Coulombic quantum fluctuations.

Zero-energy Landau levels evolve into pseudo-zero-mode levels with filling.

Comparison with experiments supports the theoretical predictions.

Abstract

In a magnetic field bilayer graphene supports an octet of zero-energy Landau levels with an extra twofold degeneracy in Landau orbitals n=0 and n=1. It is shown that this orbital degeneracy is lifted due to Coulombic quantum fluctuations of the valence band (the Dirac sea); this is a quantum effect analogous to the Lamb shift in the hydrogen atom. A detailed study is made of how these zero-energy levels evolve, with filling, into a variety of pseudo-zero-mode Landau levels in the presence of possible spin and valley breaking and Coulomb interactions, and a comparison is made with experimental results.