A Four-State Potts Model in Nb₄Se₄I₄?

Hidden order phase transitions offer open questions as to the underlying physics governing how certain quantum materials behave. Nb₄Se₄I₄ is one such material, in which a phase transition observed at T = 93K had no obvious origin. Here we propose that this phase transition is driven by a four-state Potts model whose states correspond to Jahn-Teller distortions of its network of corner-sharing Nb tetrahedra. This proposal is motivated through probes of the physical properties and average structure of Nb₄Se₄I₄, followed by an in-depth investigation of the local structure of Nb₄Se₄I₄ through high-resolution synchrotron x-ray and neutron total scattering experiments with subsequent pair distribution function analysis. The probing of the local structure is considered in two regimes: the intra-tetrahedron displacements generating the states of the model, and the interaction between neighboring tetrahedra governing the nature of the proposed model. This investigation demonstrates strong evidence of the relevant displacive modes through which the model would be realized within single tetrahedra, and offers insight into the inter-tetrahedron behavior of the model. We propose further x-ray absorption measurements combined with high-resolution x-ray total scattering experiments to definitely resolve the origin of this transition and the long-range behavior of the proposed Potts model.