Low-temperature acanthite-like phase of Cu$_{2}$S: A first-principles study on electronic and transport properties

The mobility and disorder in the lattice of Cu atoms as liquid-like behavior is an important characteristic affecting the thermoelectric properties of Cu$_{2}$S. In this study, using a theoretical model called acanthite-like structure for Cu$_{2}$S at a low-temperature range, we systematically investigate the electronic structure, intrinsic defect formation, and transport properties by first-principles calculations. Thereby, previous experimental reports on the indirect bandgap nature of Cu$_{2}$S were confirmed in this work with an energy gap of about 0.9-0.95 eV. As a result, the optical absorption coefficient estimated from this model also gives a potential value of $\alpha > 10^{4}$ cm$^{-1}$ in the visible spectrum range. According to the bonding analysis and formation energy aspect, Cu vacancy is the most preferred defect to form in Cu$_{2}$S, which primarily affects the conductive behavior as a $p$-type, as experimentally observed. Finally, the transport properties of Cu$_{2}$S system were successfully reproduced using an electron-phonon scattering method, highlighting the important role of relaxation time prediction in conductivity estimation instead of regarding it as a constant.