Non-abelian gauge fields and quadratic band touchings in molecular graphene

TL;DR

This paper explores how non-abelian gauge fields can be engineered in molecular graphene, revealing their effects on Dirac electrons, including quadratic band touchings and Landau levels, with potential for experimental observation and new quantum states.

Contribution

It demonstrates how to induce and analyze non-abelian gauge fields in molecular graphene, highlighting their unique effects on electronic spectra and measurable signatures.

Findings

Non-abelian gauge fields can create quadratic band touchings in molecular graphene.

A constant non-abelian magnetic field can produce Landau levels or quadratic band touchings.

Characteristic signatures in the density of states can be observed experimentally.

Abstract

Dirac fermions in graphene can be subjected to non-abelian gauge fields by implementing certain modulations of the carbon site potentials. Artificial graphene, engineered with a lattice of CO molecules on top of the surface of Cu, offers an ideal arena to study their effects. In this work, we show by symmetry arguments how the underlying CO lattice must be deformed to obtain these gauge fields, and estimate their strength. We also discuss the fundamental differences between abelian and non-abelian gauge fields from the Dirac electrons point of view, and show how a constant (non-abelian) magnetic field gives rise to either a Landau level spectrum or a quadratic band touching, depending on the gauge field that realizes it (a known feature of non-abelian gauge fields known as the Wu-Yang ambiguity). We finally present the characteristic signatures of these effects in the site-resolved density of states that can be directly measured in the current molecular graphene experiment, and discuss prospects to realize the interaction induced broken symmetry states of a quadratic touching in this system.