The effect of on-site and inter-site Hubbard correction in the thermoelectric properties of quaternary Heusler alloys NaHfXSn (X = Co, Rh, Ir): a first-principles study†

The Hubbard-corrected density functional theory (DFT) has been shown to effectively mitigate self-interaction errors in studying the properties of various materials. However, its effectiveness in evaluating the thermoelectric properties of non-magnetic semiconducting quaternary Heusler alloys remains largely unexplored. In this study, we apply GGA, GGA+U, and its extensions GGA+U+V, along with spin–orbit coupling (SOC), to examine the structural, electronic, elastic, thermodynamic, and thermoelectric properties of the non-magnetic NaHfXSn (X = Co, Rh, Ir) quaternary Heusler alloys. The Hubbard parameters (on-site U and inter-site V) are determined self-consistently using density-functional perturbation theory, eliminating the need for empirical inputs. For more precise optical property analysis, we use the Sternheimer method within the framework of time-dependent density functional theory (TDDFT). Our results show maximum thermoelectric efficiency (figure of merit) at 1200 K, with ZT values of approximately 1.02, 0.86, and 0.71 for X = Co, Rh, and Ir, respectively, indicating the potential of these materials for high-temperature thermoelectric device applications.