Trigonal Warping in Bilayer Graphene: Energy versus Entanglement Spectrum

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.

arXiv comment12 pages, 6 figures included, introduction expanded, pertaining references added

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• Valley polarization, magnetization, and superconductivity in bilayer graphene near the van Hove singularity
• Entanglement spectrum of fermionic bilayer honeycomb lattice: Hofstadter butterfly
• Pairwise entanglement and the Mott transition for correlated electrons in nanochains
• Entanglement Chern Number of the Kane-Mele Model with Ferromagnetism
• Phase-space elementary information content of confined Dirac spinors
• Capturing magic angles in twisted bilayer graphene from information theory markers
• Tunable Band Inversion in Trilayer Graphene
• Entanglement spectra of superconductivity ground states on the honeycomb lattice
• Complete Spin and Valley Polarization by Total External Reflection from Potential Barriers in Bilayer Graphene and Monolayer Transition Metal Dichalcogenides
• Dipole representation of composite fermions in graphene quantum Hall systems