Effect ofp1/2corrections in the electronic structure ofBi2Te3compounds

Abstract

Unlike other relativistic corrections to the Schr\"odinger equation, such as the Darwin, mass-velocity, and spin-orbit interactions (SOI), the ${p}_{1/2}$ corrections do not arise from expansion of the relativistic Dirac equation. Rather, these corrections relate to the way in which the p-orbital wave functions are expanded in density functional calculations with SOI. A test of this correction is necessary in a strongly bonded system which has significant SOI effects, such as ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}.$ Previous electronic structure calculations of ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ have disagreed about the position of the conduction band minimum (CBM). While de Haas--van Alphen experiments find the CBM to have sixfold degeneracy, most previous calculations have found this minimum to lie at a twofold degenerate point. A recent paper found the correct degeneracy, but was unable to explain the difference in their and previous results. We find the correct degeneracy by taking into account the ${p}_{1/2}$ corrections, which shifts the minimum from a twofold degenerate point to a sixfold degenerate point and is necessary for the correct degeneracy of the valence band as well. The ${p}_{1/2}$ corrections for the Sb $5p$ states are much weaker, explaining the electronic structure results in the related compounds ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3},$ ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3},$ and ${\mathrm{BiSbTe}}_{3}.$