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Quantitative analysis on electric dipole energy in Rashba band splitting.

Hong J, Rhim JW, Kim C, Ryong Park S, Hoon Shim J - Sci Rep (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry, Pohang University of Science and Technology, Pohang 790-784, Korea.

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.

No MeSH data available.


Calculated band structures.Band structure of (a) Bi single layer and (b) Sb single layer under the electric field 0.5 V/Å along the perpendicular direction to the layer. Bands 3 and 4 show the largest splitting and the others show small splitting.
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f1: Calculated band structures.Band structure of (a) Bi single layer and (b) Sb single layer under the electric field 0.5 V/Å along the perpendicular direction to the layer. Bands 3 and 4 show the largest splitting and the others show small splitting.

Mentions: We present in Fig. 1 the band structures of Bi and Sb single layers under an electric field 0.5 V/Å along the direction perpendicular to the layers. The six bands are composed of p-orbitals of Bi or Sb atoms. Bands 1 and 2 are mainly of J ≈ 1/2 character while bands 3 to 6 come from mainly J ≈ 3/2 states. We can see the Rashba splitting in the band structure near the Γ and M points which are time reversal invariant momenta (TRIM) of the triangular lattice. Bi single layer whose atomic SOC is stronger than that of Sb shows a larger Rashba splitting in its band structure, which indicates that the magnitude of the Rashba splitting is clearly related to the atomic SOC strength. Indeed, the Rashba splitting observed at Cu, Ag, and Au surfaces also show such correlation between the atomic SOC and the size of the Rashba splitting16.


Quantitative analysis on electric dipole energy in Rashba band splitting.

Hong J, Rhim JW, Kim C, Ryong Park S, Hoon Shim J - Sci Rep (2015)

Calculated band structures.Band structure of (a) Bi single layer and (b) Sb single layer under the electric field 0.5 V/Å along the perpendicular direction to the layer. Bands 3 and 4 show the largest splitting and the others show small splitting.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4555038&req=5

f1: Calculated band structures.Band structure of (a) Bi single layer and (b) Sb single layer under the electric field 0.5 V/Å along the perpendicular direction to the layer. Bands 3 and 4 show the largest splitting and the others show small splitting.
Mentions: We present in Fig. 1 the band structures of Bi and Sb single layers under an electric field 0.5 V/Å along the direction perpendicular to the layers. The six bands are composed of p-orbitals of Bi or Sb atoms. Bands 1 and 2 are mainly of J ≈ 1/2 character while bands 3 to 6 come from mainly J ≈ 3/2 states. We can see the Rashba splitting in the band structure near the Γ and M points which are time reversal invariant momenta (TRIM) of the triangular lattice. Bi single layer whose atomic SOC is stronger than that of Sb shows a larger Rashba splitting in its band structure, which indicates that the magnitude of the Rashba splitting is clearly related to the atomic SOC strength. Indeed, the Rashba splitting observed at Cu, Ag, and Au surfaces also show such correlation between the atomic SOC and the size of the Rashba splitting16.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry, Pohang University of Science and Technology, Pohang 790-784, Korea.

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.

No MeSH data available.