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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.


SAM and OAM of Bi triangular lattice under the field.SAM and OAM of bands 1 to 6 of Bi triangular lattice near the Γ point are shown in (b). The numbers indicate the band indices shown in Fig. 1. Red arrows are SAM and blue arrows are OAM. The  space region for (b) is shown in (a) as dotted square.
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f2: SAM and OAM of Bi triangular lattice under the field.SAM and OAM of bands 1 to 6 of Bi triangular lattice near the Γ point are shown in (b). The numbers indicate the band indices shown in Fig. 1. Red arrows are SAM and blue arrows are OAM. The space region for (b) is shown in (a) as dotted square.

Mentions: In Fig. 2, we plot the expectation values of in-plane components of SAM and OAM of the Bi single layer near the Γ point. The SAM and OAM for Sb single layer (not shown here) have the same trends as those of Bi single layer. The only difference is the smaller OAM magnitude for Sb compared with Bi, which might be the result of the small SOC in Sb. All the OAM patterns of the bands show chiral structures around the Γ point and the chiral directions of adjacent bands are opposite to each other. SAM also has similar patterns to those of OAM because of the strong SOC. SAM for J ≈ 1/2 bands (bands 1 and 2) are antiparallel to OAM while they are almost parallel to the OAM directions in J ≈ 3/2 bands (bands 3 to 6).


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)

SAM and OAM of Bi triangular lattice under the field.SAM and OAM of bands 1 to 6 of Bi triangular lattice near the Γ point are shown in (b). The numbers indicate the band indices shown in Fig. 1. Red arrows are SAM and blue arrows are OAM. The  space region for (b) is shown in (a) as dotted square.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: SAM and OAM of Bi triangular lattice under the field.SAM and OAM of bands 1 to 6 of Bi triangular lattice near the Γ point are shown in (b). The numbers indicate the band indices shown in Fig. 1. Red arrows are SAM and blue arrows are OAM. The space region for (b) is shown in (a) as dotted square.
Mentions: In Fig. 2, we plot the expectation values of in-plane components of SAM and OAM of the Bi single layer near the Γ point. The SAM and OAM for Sb single layer (not shown here) have the same trends as those of Bi single layer. The only difference is the smaller OAM magnitude for Sb compared with Bi, which might be the result of the small SOC in Sb. All the OAM patterns of the bands show chiral structures around the Γ point and the chiral directions of adjacent bands are opposite to each other. SAM also has similar patterns to those of OAM because of the strong SOC. SAM for J ≈ 1/2 bands (bands 1 and 2) are antiparallel to OAM while they are almost parallel to the OAM directions in J ≈ 3/2 bands (bands 3 to 6).

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.