First-Principles Design of a Half-Filled Flat Band of the Kagome Lattice in Two-Dimensional Metal-Organic Frameworks

TL;DR

This paper designs a two-dimensional metal-organic framework with a flat band exhibiting ferromagnetism and non-trivial topology, combining first-principles calculations and tight-binding models.

Contribution

It introduces a novel MOF with a half-filled flat kagome band that is both ferromagnetic and topologically non-trivial, realized through first-principles design.

Findings

Identification of trans-Au-THTAP as an ideal flat-band MOF

Observation of a non-zero Chern number due to spin-orbit coupling

Presence of edge states confirming topological properties

Abstract

We design from first principles a new type of two-dimensional metal-organic frameworks (MOFs) using phenalenyl-based ligands to exhibit a half-filled flat band of the kagome lattice, which is one of the lattice family that shows Lieb-Mielke-Tasaki's flat-band ferromagnetism. Among various MOFs, we find that $\textit{trans}$-Au-THTAP(trihydroxytriaminophenalenyl) has such an ideal band structure, where the Fermi energy is adjusted right at the flat band due to unpaired electrons of radical phenalenyl. The spin-orbit coupling opens a band gap giving a non-zero Chern number to the nearly flat band, as confirmed by the presence of the edge states in first-principles calculations and by fitting to the tight-binding model. This is a novel and realistic example of a system in which a nearly flat band is both ferromagnetic $\textit{and}$ topologically non-trivial.