An equivalence between monolayer and bilayer honeycomb lattices

TL;DR

This paper demonstrates an equivalence between the tight-binding models of monolayer and bilayer honeycomb lattices, revealing that with specific parameters, their Hamiltonians are effectively identical, especially considering trigonal warping effects.

Contribution

It establishes a theoretical equivalence between monolayer and bilayer honeycomb lattice descriptions, highlighting the role of third nearest neighbors in this correspondence.

Findings

Hamiltonians are equivalent with appropriate parameters

Third nearest neighbors coupling is crucial

Provides a physical explanation for the equivalence

Abstract

In this brief report, we show the equivalence between the tight-binding descriptions of the monolayer and bilayer honeycomb lattices. With appropriate value of the third nearest neighbors coupling, the Hamiltonian for a monolayer is equivalent to the low energy effective Hamiltonian for bilayer in the presence of trigonal warping. A simple physical argument is provided to explain this correspondance.