Honeycomb anti-dot artificial lattice as a prototypical correlated Dirac fermions system

TL;DR

This paper theoretically investigates an artificial honeycomb lattice in a two-dimensional electron gas, emphasizing how electron-electron interactions and screening influence the emergence of correlated phenomena like antiferromagnetic order and insulating states.

Contribution

It introduces a model incorporating electron-gas self-screening effects, highlighting the importance of anti-dot radius in achieving correlated Dirac fermion behavior in artificial lattices.

Findings

Electron-electron interactions are significant in the system.

Screening effects are essential to match experimental observations.

Specific anti-dot sizes promote correlated insulating and magnetic states.

Abstract

We study theoretically the electronic properties of the artificial quantum dot honeycomb lattice defined in a two-dimensional electron gas, focusing on the possibility of achieving a regime in which electronic correlations play a dominant role. At first we establish a non-interacting model compatible with recently studied experimentally devices. According to the values of the obtained electron-electron interaction integrals, we postulate that the inclusion of inherent electron-gas self-screening is indispensable to reconstruct the experimental observations. Applying the Thomas-Fermi type of screening, we show that the radius of the anti-dot is crucial to achieve a correlated state in which phenomena like antiferromagentic ordering and interaction-induced insulating state appear. We estimate the conditions for which the electronically correlated state in an artificial honeycomb lattice can be realized.