Unraveling the origins of conduction band valley degeneracies in Mg₂Si_1-xSn_x thermoelectrics

To better understand the thermoelectric efficiency of the Mg-based thermoelectrics, using hybrid density-functional theory, we study the microscopic origins of valley degeneracies in the conduction band of the solid solution Mg₂Si_1-xSn_x and its constituent components - namely, Mg₂Si and Mg₂Sn. In the solid solution of Mg₂Si_1-xSn_x, the sublattices are expected to undergo either tensile or compressive strain in the light of Vegard's law. Interestingly, we find both tensile strain of Mg₂Si and compressive strain of Mg₂Sn enhance the conduction band valley degeneracy. We suggest that the optimal sublattice strain as one of the origins of the enhanced Seebeck coefficient in the Mg₂Si_1-xSn_x system. In order to visualize the enhanced band valley degeneracy at elevated temperatures, the ground state eigenvalues and weights are projected by convolution functions that account for high temperature effects. Our results provide theoretical evidences for the role of sublattice strain in the band valley degeneracy observed in Mg₂Si_1-xSn_x.