Diradicals as Topological Charge Carriers in Metal-Organic Toy Model Pt₃(HAB)₂

We explore the eclipsed stacking of a metal-organic Kagome lattice containing heavy-metal nodes. Our model is Pt3(HAB)2, a hypothetical but viable member of a well-known family of hexaaminobenzene (HAB) based metal-organic frameworks (MOFs). Applying space group theory, it is shown how molecular diradicals, brought into play by a non-innocent ligand, become topologically nontrivial bands when moving in a periodic potential. Three factors are required to enable this: 1) eclipsed stacking, which shifts the Fermi level near a symmetry-protected band crossing 2) the emergence of an electride-like ‘pore band’ that renders the topological Z_2 invariant equal to 1, thus nontrivial, and 3) Pt-induced spin-orbit coupling, to turn the crossing into a bulk band gap.<br/>For this MOF, as should be the case for this entire family of MOFs, the Kagome band dispersion is controlled through (weak) π* antibonding interactions between ligand and metal. These interactions mediate superexchange, through the metal node, between diradicals localized on the organic struts. In the scenario of highly ordered, eclipsed stacking, the Fermi level shifts to a position where these levels belong to free framework charge carriers. We predict the Kagome band to shape Dirac cones, which become gapped in the presence of strong spin-orbit coupling, brought upon the system by Pt. An analysis of the topological Z_2 invariant suggests that robust topological surface states must appear within that gap. There is a special role for the pore band, itself an apparent case of nonlocality. This highly delocalized band describes charge density that is not centered around nuclei, but rather within the tubular pores of the system, and between layers. Strongly related to the well-known interlayer band, it plays a significant role in rendering the system topologically nontrivial, i.e., without pore band, the Z_2 invariant would be equal to zero. The pore band should be of interest to various applications, including catalysis and superconductivity. And a porous topological semimetal, like this framework, should offer new opportunities for quantum materials. For example, if topological surface states would emerge on the interior surface, i.e., the pore, filling the pores of the MOF with an appropriate substrate would constitute a novel way of creating an interface between domains.<br/>The direct connection between diradical chemistry and topological states gives chemical control over nonlocal physics; we know states to becomes more delocalized upon increasing the diradical character, which we know scales with S &lt; NH &lt; O for organic linker substituents. Given MOFs and their building blocks are highly tunable, this could pave the wave to tailored topological electronics. We hope this work motivates the pursuit of synthesizing highly perfect, electronically conductive MOF crystals. Eclipsed-stacked Pt3(HAB)2 is a toy model, but a realistic one. Its realization would be highly compelling for a variety of electronic applications.