Effective low energy Hamiltonians and unconventional Landau level spectrum of monolayer C$_3$N

TL;DR

This paper derives low-energy Hamiltonians for monolayer C$_3$N, analyzes its electronic symmetries, and explores its Landau level spectrum, revealing similarities to bilayer graphene and potential for electron-electron interactions.

Contribution

It provides the first derivation of effective Hamiltonians at key points in the Brillouin zone for monolayer C$_3$N and analyzes its Landau levels, connecting theory with recent ab-initio results.

Findings

Landau level spectrum shows bilayer graphene-like properties.

Heavy effective mass suggests possible electron-electron interaction effects.

Analysis clarifies optical properties consistent with ab-initio calculations.

Abstract

We derive a low-energy effective $\mathbf{k}\cdot\mathbf{p}$ Hamiltonians for monolayer C$_{3}$N at the $ \Gamma $ and $ M $ points of the Brillouin zone where the band edge in the conduction and valence band can be found. Our analysis of the electronic band symmetries helps to better understand several results of recent ab-initio calculations[1,2] for the optical properties of this material. We also calculate the Landau level spectrum. We find that the Landau level spectrum in the degenerate conduction bands at the $ \Gamma $ point acquires properties that are reminiscent of the corresponding results in bilayer graphene, but there are important differences as well. Moreover, because of the heavy effective mass, $n$-doped samples may host interesting electron-electron interaction effects.