Effect of the Spin-Orbit Interaction on the Thermodynamic Properties of Crystals: Specific Heat of Bismuth

Abstract

We discuss measurements and ab initio calculations of the specific heat for crystalline bismuth, strictly speaking, a semimetal but in the temperature region accessible to us ($T>2\mathrm{K}$) acting as a semiconductor. We extend experimental data available in the literature and notice that the ab initio calculations without spin-orbit interaction exhibit a maximum at $\sim 8\mathrm{K}$, about 20% lower than the measured one. Inclusion of spin-orbit interaction decreases the discrepancy markedly: the maximum of $C(T)$ is now only 7% larger than the measured one. Exact agreement is obtained if the strength of the spin-orbit Hamiltonian is reduced by a factor of $\sim 0.9$. We also discuss the dependence of the lattice parameter and the cohesive energy on spin-orbit interaction.