Ti 3d Electronic States of Hollandite-type Ba_xTi₈O_16+δ Studied by Cluster-Model and Band-Structure Calculations

We report results of cluster-model and band-structure calculations for hollandite-type Ba_xTi₈O₁₆₊δ. In the band-structure calculations, the quasi one-dimensional band structure (dispersive along the c-axis) provides anisotropic transport behaviors which are consistent with the experimental results reported by Murata et al. for the metallic phase [Phys. Rev. B 92, 220408(R) (2015)]. The resistivity and the magnitude of the Seebeck coefficient along the c-axis are smaller than those along the a- and b-axes. On the other hand, good agreement between the cluster-model calculation and the Ti 2p photoemission spectrum indicates localized nature of the Ti 3d electrons. While the transport behavior is well described by the itinerant model, the excitation spectrum is consistent with the localized model. We argue that the polaronic effect is responsible for the dual nature of the Ti 3d electrons in Ba_xTi₈O₁₆₊δ.