Phonon band structure and interatomic force constants for bismuth: Crucial role of spin-orbit interaction

The dynamical properties and the interatomic force constants for bismuth (Bi) are investigated from first principles with the use of density functional theory. In this context, Bi has two striking characteristics: it is a semimetal with a very small carrier density, and the spin-orbit (SO) coupling is particularly strong. To decouple these characteristics, we treat Bi as (i) nonmetallic without SO interaction, (ii) metallic with, and (iii) without SO interaction. Phonon dispersion relations and interatomic force constants are reported and compared with available experimental data, and very good agreement is obtained only when SO interaction is taken into account: removing this interaction causes a difference on the order of 10% in the phonon frequencies and interatomic force constants. Such a difference is also present in the ${\mathrm{Bi}}_2$ molecule. We also determine which phonon bands are more affected directly by the SO interaction and which bands are indirectly affected, through changes in cell parameters. The dependence of the latter with respect to the SO coupling is also reported.