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

Source: [Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene](<https://www.sota2.com/research/paper/68fa2bae1e209131ce849407>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:53:15.035Z

Authors: K. Shizuya

Published: 2012-05-29T11:16:28.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1205.6330>)

[PDF](<https://arxiv.org/pdf/1205.6330.pdf>)