Figure 3: Three-dimensional orbital and spin texture of the topological and 2DEG states.
From: Emergent quantum confinement at topological insulator surfaces
(a,b) Circular dichroism in constant energy contours and E versus k dispersions measured by ARPES encode the spin–orbital texture of the topological (outer band) and 2DEG (remaining features) states. Circular dichroism along Γ–M (b), extracted along the bold green line shown in a, contains only the in-plane component. This reveals opposite helicity for consecutive Fermi surface sheets, with the spin pointing into (
) or out of (
) the plane of the figure. (c) Quantitative analysis of the angular dependence of the dichroism around the Fermi surface, shown for the outer branch of the lowest Rashba-split 2DEG state as a function of aziumthal angle, φ, from the dashed green line (Γ–M, ky=0) direction shown in a. Error bars reflect an approximate estimate of the uncertainty in extracting the asymmetry parameter from the experimental measurements, incorporating statistical errors in peak fitting, systematic errors and sample-to-sample variations. The fit to the total dichroism (black line) contains not only a component which varies as sin(φ) (yellow), but also a large sin(3φ) contribution (blue), revealing a significant out-of-plane orbital, and therefore also spin, canting. This is consistent with our calculations shown in d (see also Supplementary Fig. S5), which reveal an alternating helical texture of both the orbital and spin angular momenta (absolute magnitude represented by the false colour scale to the right), but with opposite winding direction. These develop significant out-of-plane components for the larger Fermi surface sheets. In contrast, our calculations and experiment reveal that all other states largely retain the in-plane spin texture characteristic of classic Rashba systems all the way up to the Fermi energy. Together, this leads to a rich three-dimensional spin-texture of the surface electronic structure of topological insulators, as summarized by the arrows on the TSS (blue) and lowest Rashba-split (brown-green) subband of the 2DEG in e.
