Presence of Bismuth (Bi) leads to topologically nontrivial band structure in many materials, especially in topological insulators. Traditionally Bi is known to be a semimetal but, quite surprisingly, in a recent experiment bulk Bi has been found to be a superconductor below 0.53 mK at ambient pressure. In order to have a closer look at the electronic properties of bulk Bi in the wake of this unexpected experimental evidence of superconducting phase, we have performed density-functional-theory (DFT) based first principle calculations using plane-wave basis set and with suitable ionic pseudopotentials. We have computed the band structure, density of states and Fermi surfaces for two different type of exchange-correlation (XC) functionals, namely Perdew-Zunger (PZ) and Perdew-Burke-Ernzerhof (PBE) type. Each of these XC functional has been considered without and with spin orbit (SO) interaction. After carefully examining the energy-convergence with respect to plane wave basis set and k-points in each case, the band structure has been calculated along the path Γ-L-T-Γ. Without SO coupling, electron pocket is found near ‘L’ and exactly at ‘Г’ and hole pocket is at ‘T’ for PZ type XC functional, while in the case of PBE-type electron pocket is found exactly at ‘L’ but the hole pocket to be near to ‘T’. With SO coupling, in PZ-type, electron pocket remains at same position, but hole pocket appears only at ‘Г’ point. Finally, when SO coupling is taken into account along with PBE-type XC functional electrons and holes are found at ‘L’ and at ‘T’ respectively. Furthermore, in this case we also observe an increase in the number of holes at ‘T’.
Massively parallel, linear-scaling Hartree-Fock exchange and hybrid exchange-correlation functionals with plane-wave basis set accuracy
