Definition of a material's quasi-dimensionality using the electronic structure

We formulate a way to define the quasi-dimensionality of a material given its electronic structure. Our definition provides a more nuanced description of quasi-dimensionality that cannot be obtained from the analysis of the interatomic distances, or crystal structure, alone. For example, using first-principles calculations, we show that the nominally quasi-two-dimensional layered material LaTe$_3$ is better described as an assembly of interwoven quasi-one-dimensional chains. This view is consistent with the observation of the charge density wave state in LaTe$_3$. Our formulation of quasi-dimensionality relies on analyzing the time dependence of Wannier states whose spread is minimized over a time interval.