Temperature dependence of spin-orbit coupling effect in solids

The spin-orbit coupling (SOC) effect is a relativistic effect that is strongly expressed in valence electrons and therefore significantly affects the band structure of solids. Studies on the SOC effect are usually not concerned with its dependence on temperature. Here, using first-principles calculations assisted with molecular-dynamics simulations, we show that the band gap correction due to the SOC (AEg) is strongly temperature dependent. Taking PbTe as the example, we found that AEg can decrease by about 0.25 eV when temperature increases from 300 to 1100 K. Considering that the commonly adopted experimental band gap is about 0.3 eV for PbTe, this temperature dependence of AEg is significant. The origin of this dependence can be clearly traced to the evolution of the conduction-band minimum state. As the temperature increases, the state becomes less delocalized, which weakens the SOC. This finding is expected to be generally applicable to other semiconductor materials containing elements of high atomic numbers. Future computational studies on such materials, especially for high-temperature applications, would be suggested to carefully include the temperature dependence of SOC.