Excitonic effects in the optical absorption of gapless semiconductor α-tin near the direct bandgap

Most cubic semiconductors have threefold degenerate p-bonding valence bands and nondegenerate s-antibonding conduction bands. This allows strong interband transitions from the valence to the conduction bands. On the other hand, intervalence band transitions within p-bonding orbitals in conventional p-type semiconductors are forbidden at k=0 and, therefore, weak, but observable. In gapless semiconductors, however, the s-antibonding band moves down between the split-off hole band and the valence band maximum due to the Darwin shift. This band arrangement makes them three-dimensional topological insulators. It also allows strong interband transitions from the s-antibonding valence band to the p-bonding bands, which have been observed in α-tin with Fourier-transform infrared spectroscopic ellipsometry [Carrasco et al., Appl. Phys. Lett. 113, 232104 (2018)]. This manuscript presents a theoretical description of such transitions applicable to many gapless semiconductors. This model is based on k→⋅p→ theory, degenerate carrier statistics, the excitonic Sommerfeld enhancement, and screening of the transitions by many-body effects. The impact of nonparabolic bands is approximated within Kane’s 8×8k→⋅p→-model by adjustments of the effective masses. This achieves agreement with experiments.