Influence of internal displacement on band structure, phase transition, and thermoelectric properties of bismuth

First principles calculation and Boltzmann transport theory have been combined to investigate the fundamental influence of internal displacement (u) on lattice stability, band structure, phase transition, and thermoelectric properties of Bi. Calculation reveals that Bi could keep its ground-state rhombohedral structure and mechanical stability within the entire studied range of u (0.2150 ≤ u ≤ 0.2500). It is also shown that the phase transitions of semimetal–semiconductor, semiconductor–semimetal, and semimetal–metal of Bi can happen at the critical u points of 0.2184, 0.2325, and 0.2400, respectively, which are mainly ascribed to the changes of the symmetry points of T, Γ, and L with the increase of u. In addition, the highest Seebeck coefficient of Bi could be achieved when u equals 0.2250 due to the lowest carrier density and is much bigger than the corresponding value of equilibrium Bi (u = 0.2357). The obtained results are in good agreement with experimental observations in the literature and could deepen the understanding of the fundamental relationship between internal displacement, band structure, phase transition, and Seebeck coefficient of Bi.