Trigonal Warping in Bilayer Graphene: Energy versus Entanglement Spectrum

TL;DR

This paper analytically studies the entanglement spectrum of Bernal-stacked bilayer graphene with trigonal warping, revealing geometric differences from monolayer spectra but consistent topological properties, and provides full eigensystem expressions.

Contribution

It offers the first analytical expressions for the full eigensystem of bilayer graphene with trigonal warping across the entire Brillouin zone.

Findings

Entanglement spectrum differs geometrically from monolayer energy spectrum.

Topological quantities like Berry phase remain consistent.

Provides analytical eigensystem expressions for the entire Brillouin zone.

Abstract

We present a mainly analytical study of the entanglement spectrum of Bernal-stacked graphene bilayers in the presence of trigonal warping in the energy spectrum. Upon tracing out one layer, the entanglement spectrum shows qualitative geometric differences to the energy spectrum of a graphene monolayer. However, topological quantities such as Berry phase type contributions to Chern numbers agree. The latter analysis involves not only the eigenvalues of the entanglement Hamiltonian but also its eigenvectors. We also discuss the entanglement spectra resulting from tracing out other sublattices. As a technical basis of our analysis we provide closed analytical expressions for the full eigensystem of bilayer graphene in the entire Brillouin zone with a trigonally warped spectrum.