Dimensionality-driven evolution of electronic structure and transport properties in pressure-induced phases of Ca$_2$N electride

We investigate how a change in dimensionality of interstitial electronic states in the Ca$_2$N electride influences its electronic structure and transport properties. Employing the Maximally Localized Wannier Functions (MLWF) approach, we successfully describe the interstitial quasi-atomic states (ISQ) located in non-nuclear Wyckoff positions between Ca atoms. This allowed us to conclude that the electride subsystem is responsible for the formation of a band structure in the vicinity of the Fermi level in all Ca$_2$N phases observed under pressure. Using the obtained MLWF basis, we calculate the electronic and thermal conductivity, along with the Seebeck coefficient, by solving the semi-classical Boltzmann transport equations. The results achieved permit the conclusion that the counterintuitive increase in resistance under pressure observed experimentally is attributed to enhanced localization of interstitial electronic states through electride subspace dimensionality transformations. We also established a substantial anisotropy in the transport properties within the 2D phase and found that the conductivity inside the plane of the electride layers is provided by electrons, while along the direction normal to the layers, holes become the majority carriers.