Effect of the spin-orbit interaction on the thermodynamic properties of crystals: specific heat of bismuth

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 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 approximately 8 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 approximately 0.9. We also discuss the dependence of the lattice parameter and the cohesive energy on spin-orbit interaction.