Quartic energy band engineering in artificial semiconductor honeycomb lattices

TL;DR

This paper explores how to engineer quartic energy dispersions in artificial honeycomb lattices, revealing conditions for different quartic band types and demonstrating the potential for tailored electronic properties in artificial graphene systems.

Contribution

It introduces a classification of quartic band types in artificial graphene and shows how lattice geometry influences their emergence, advancing band structure engineering.

Findings

Three types of quartic bands identified: MHS, purely quartic, non-MHS.

Staggered honeycomb supports all three quartic band types.

Planar honeycomb yields only two quartic band types.

Abstract

Artificially engineered lattices provide a flexible platform for reproducing and extending the electronic behavior of atomic-scale materials. Artificial graphene systems, in particular, mimic graphene-like linear dispersion with tunable Dirac cones and offer a route to realizing more exotic band structures. Here we examine the emergence of quartic energy dispersion in artificial graphene heterostructures using analytical modeling and numerical solutions of the effective Hamiltonian. We identify three distinct quartic band types: Mexican-hat-shaped (MHS), purely quartic, and non-MHS quartic bands, and determine the conditions under which each arises. We find that a staggered honeycomb lattice supports all three classes of quartic dispersion, whereas its planar counterpart yields only purely quartic and non-MHS forms. These results demonstrate the feasibility of engineering quartic band edges in artificial lattices and clarify how lattice geometry can be used to tailor their characteristics.