Perovskite ThTaN3: a Large Thermopower Topological Crystalline Insulator

ThTaN$_3$, a rare cubic perovskite nitride semiconductor, has been studied using {\it ab initio} methods. Spin-orbit coupling (SOC) results in band inversion and a band gap of 150 meV at the zone center. In spite of the trivial $Z_2$ indices, two pairs of spin-polarized surface bands cross the gap near the zone center, indicating that this system is a topological crystalline insulator with the mirror Chern number of $|{\cal C}_m|=2$ protected by the mirror and $C_4$ rotational symmetries. Additionally, SOC doubles the Seebeck coefficient, leading to a maximum of $\sim$400 $\mu$V/K at 150 K for carrier-doping levels of several $10^{17}$/cm$^3$. ThTaN$_3$ combines excellent bulk thermopower with parallel conduction through topological surface states that provide a platform for large engineering devices with ever larger figures of merit.