Abstract
We report on quantitative comparison between the electric dipole energy and the Rashba band splitting in model systems of Bi and Sb triangular monolayers under a perpendicular electric field. We used both first-principles and tight binding calculations on p-orbitals with spin-orbit coupling. First-principles calculation shows Rashba band splitting in both systems. It also shows asymmetric charge distributions in the Rashba split bands which are induced by the orbital angular momentum. We calculated the electric dipole energies from coupling of the asymmetric charge distribution and external electric field, and compared it to the Rashba splitting. Remarkably, the total split energy is found to come mostly from the difference in the electric dipole energy for both Bi and Sb systems. A perturbative approach for long wave length limit starting from tight binding calculation also supports that the Rashba band splitting originates mostly from the electric dipole energy difference in the strong atomic spin-orbit coupling regime.
Highlights
Angle-resolved photoemission (ARPES)[10,11,14,15]
The outcome from the interaction between the asymmetric charge distribution and the electric field is responsible for the Rashba band splitting in Bi and Sb monolayers
We confirm that the Rashba band splitting mostly originates from the electric dipole energy difference in both Bi and Sb layers, which are considered as in the strong spin-orbit coupling (SOC) regime
Summary
The electric dipole energy difference is larger than the Rashba band splitting in Bi layer It is mainly because of the screening effect. We confirm that the Rashba band splitting mostly originates from the electric dipole energy difference in both Bi and Sb layers, which are considered as in the strong SOC regime. We regard hISB(k) as a perturbation to explain the splitting of two degenerate multi-orbital bands by the ISB This is a more general consideration compared with the previous section and its results hold throughout whole Brillouin zone if γ is much smaller than the spin-orbit interaction.
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