Tunable Bi-frustrated Electron Spin and Charge States in a Cu-Hexaaminobenzene Framework

TL;DR

This paper reports on a Cu-Hexaaminobenzene metal-organic framework that hosts coexisting frustrated electron spin and charge states, tunable via doping, offering a platform to explore novel quantum phases.

Contribution

It introduces a new Cu-Hexaaminobenzene framework exhibiting both frustrated spin and charge states, and demonstrates tunability between these states through doping.

Findings

Cu$^{2+}$ ions form an antiferromagnetic kagome lattice.

Organic ligands create dispersionless energy bands near the Fermi level.

System can be tuned between frustrated spin and charge states by doping.

Abstract

A geometrically frustrated lattice may host frustrated electron spin or charge states that spawn exotic quantum phases. We show that a newly synthesized metal-organic framework of Cu-Hexaaminobenzene [Cu$_3$(HAB)$_2$] exhibits a multi spectra of unusual quantum phases long sought after in condensed matter physics. On one hand, the Cu$^{2+}$ ions form an ideal $S$-1/2 antiferromagnetic kagome lattice. On the other hand, the conjugated-electrons from the organic ligands give rise to completely dispersionless energy bands around the Fermi level, reproducing a frustrated $\pi_x$-$\pi_y$ hopping model on a honeycomb lattice. We propose to characterize the coexistence of frustrated local spins and conjugated electrons through scanning tunneling microscopy simulations. Most remarkably, their close energy proximity enables one to tune the system between the two frustrated states by doping up to one hole per HAB unit. Thus, Cu$_3$(HAB)$_2$ provides a unique exciting platform to investigate the interplay of frustrated spins and electrons in one single lattice, e.g. by gating experiments, which will undoubtedly raise interesting theoretical questions leading to possible new condensed-matter phases.