Reducible Fermi surface for multi-layer quantum graphs including stacked graphene
Abstract
We construct two types of multi-layer quantum graphs (Schr\"odinger operators on metric graphs) for which the dispersion function of wave vector and energy is proved to be a polynomial in the dispersion function of the single layer. This leads to the reducibility of the algebraic Fermi surface, at any energy, into several components. Each component contributes a set of bands to the spectrum of the graph operator. When the layers are graphene, AA-, AB-, and ABC-stacking are allowed within the same multi-layer structure. Conical singularities (Dirac cones) characteristic of single-layer graphene break when multiple layers are coupled, except for special AA-stacking. One of the tools we introduce is a surgery-type calculus for obtaining the dispersion function for a periodic quantum graph by gluing two graphs together.
Keywords
Cite
@article{arxiv.2005.13764,
title = {Reducible Fermi surface for multi-layer quantum graphs including stacked graphene},
author = {Lee Fisher and Wei Li and Stephen P. Shipman},
journal= {arXiv preprint arXiv:2005.13764},
year = {2021}
}