Polarons in reduced cesium tungsten bronzes studied using the DFT + U method

Abstract

To elucidate the mechanism of low-energy optical properties of Cs-doped hexagonal tungsten bronzes (Cs-HTBs), energy band structures and dielectric functions were derived via first-principle calculation using the DFT + U method. The calculated dielectric functions agreed well with the experimental values, and the 1.6-eV peak in the imaginary part of the dielectric function appeared only when oxygen vacancies were introduced into a perfect crystal. With the introduction of oxygen vacancies, localized states were formed in the lower part of the conduction band. The near-infrared absorption of Cs-HTB thus comprised localized surface plasmon resonance due to free electrons supplied by Cs and polaron absorption due to localized electrons supplied by oxygen vacancies.