Orbital-symmetry-selective spin characterization of Dirac-cone-like state on W(110)

The surface of W(110) exhibits a spin-orbit-induced Dirac-cone-like surface state, which is of mainly $d_{z^2}$ orbital character near $\overline{\mathrm{\Gamma }}$, although it is strongly influenced by the twofold ${\mathrm{C}}_{2v}$ surface symmetry. Its distinctive k-dependent spin polarization along $\overline{\mathrm{\Gamma }}\overline{\mathrm{H}}$ is revealed by spin- and angle-resolved photoemission excited with $p$- and $s$-polarized light. The spin texture of the surface state is found to change sign upon switching from $p$- to $s$-polarized light. Based on electronic-structure calculations, this behavior is explained by the orbital composition of the Dirac-cone-like state. The dominant part of the state has even mirror symmetry and is excited by $p$-polarized light. A minor part with odd symmetry is excited by $s$-polarized light and exhibits a reversed spin polarization. Our study demonstrates in which way spin-orbit interaction combines the spin degree of freedom with the orbital degree of freedom and opens a way to manipulate the spin information gathered from the Dirac-cone-like surface state by light. Our results prove that “spin control” is not restricted to topological surface states with $p$-type orbital symmetry in topological insulators.

Figure 1

ARPES results for W(110) along $\overline{\mathrm{\Gamma }}\overline{\mathrm{H}}$ obtained for $p$- and $s$-polarized light of $h\nu =43$ eV at BL-1 [(a) and (b)] and BL-9B [(c) and (d)]. The photoemission intensities are presented as contour plots $E\left({\mathbf{k}}_{\parallel }\right)$ on a linear gray scale as well as energy distribution curves (EDCs) for selected emission angles $\theta =0^{\circ },\pm 1.1^{\circ },\pm 2.4^{\circ }$, corresponding to $k_{\parallel }$ values as indicated by dashed lines.

Figure 2

Spin-integrated and spin-resolved EDCs for W(110) along $\overline{\mathrm{\Gamma }}\overline{\mathrm{H}}$ obtained with $p$-polarized (a) and nominal $s$-polarized light (b) at BL-9B. Panel (c) shows the results where the $p$ contribution has been removed from the spectra obtained with nominal $s$-polarized light. See text for details.

Figure 3

Spin-integrated and spin-resolved ARPES intensities calculated for W(110) along $\overline{\mathrm{\Gamma }}\overline{\mathrm{H}}$ within the one-step model of photoemission. Note that the intensities for $p$-polarized light are about 10 times higher than for $s$-polarized light. Panels (a)–(c) [(d)–(f)] show the calculated spectra excited by the photon energy of 43 eV with $p$- $(s$-)polarized light. [(b) and (e)] Intensity differences between spin-up and spin-down excited by $p$- and $s$-polarized light, respectively. [(c) and (f)] spin-resolved EDC spectra with several emission angles.