Role of Exchange-Correlation Functional in Bulk Bismuth

Abstract

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’.