## Unraveling the spin structure of unoccupied states in Bi2Se3

Phys. Rev. B **95**, 115401 (2017).

The optical control of spin currents in topological surface states opens new perspectives in (opto-) spintronics. To understand these processes, a profound knowledge about the dispersion and the spin polarization of both the occupied and the unoccupied electronic states is required. We present a joint experimental and theoretical study on the unoccupied electronic states of the topological insulator Bi2Se3. We discuss spin- and angle-resolved inverse-photoemission results in comparison with calculations for both the intrinsic band structure and, within the one-step model of (inverse) photoemission, the expected spectral intensities. This allows us to unravel the intrinsic spin texture of the unoccupied bands at the surface of Bi_{2}Se_{3}.

## Spin-orbit and anisotropy effects in unoccupied bulk, surface, and image-potential states on W(110)

Phys. Rev. B **95**, 085416 (2017).

We report on joint experimental and theoretical investigations of the unoccupied surface electronic structure of W(110). The spin-resolved inverse-photoemission experiments reveal a number of bands influenced by spin-orbit interaction and an image-potential state. The bands disperse differently within the two nonequivalent mirror planes of the surface, which is explained by their origin and their localization within the surface region. Surprisingly, the image-potential state also exhibits anisotropic dispersion, although it is strongly located within the surface barrier. The experimental findings are confirmed by first-principles electronic-structure calculations.

## Existence of topological nontrivial surface states in strained transition metals: W, Ta, Mo, and Nb

Phys. Rev. B **94**, 155132 (2016).

We show that a series of transition metals with strained body-centered cubic lattice—W, Ta, Nb, and Mo—hosts surface states that are topologically protected by mirror symmetry and, thus, exhibits nonzero topological invariants. These findings extend the class of topologically nontrivial systems by topological crystalline transition metals. The investigation is based on calculations of the electronic structures and of topological invariants. The signatures of a Dirac-type surface state in W(110), e.g., the linear dispersion and the spin texture, are verified. To further support our prediction, we investigate Ta(110) both theoretically and experimentally by spin-resolved inverse photoemission: unoccupied topologically nontrivial surface states are observed.

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

Phys. Rev. B **93**, 161403(R) (2016).

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

**Γ**, although it is strongly influenced by the twofold

**C**surface symmetry. Its distinctive

_{2v}**k**-dependent spin polarization along

**ΓH**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.

## Effects of orbital composition in a pair of spin-orbit-split surface bands at Tl/Ge(111)

Phys. Rev. B **93**, 085412 (2016).

The spin texture of the unoccupied surface electronic structure of the metal-semiconductor hybrid system Tl/Ge(111)−(1×1) is investigated by spin- and angle-resolved inverse photoemission as well as quasiparticle band-structure calculations. Spin-polarized surface bands with rotating spin and giant energy splitting are found along ΓK(K′), forming valleys with alternating out-of-plane spin polarization at K and K′. This behavior is known from the equivalent hybrid system on Si(111). Along ΓM, a pair of surface bands appears within a projected bulk band gap, whose equivalent on Tl/Si(111) is a surface resonance because, there, it overlaps with bulk states. Surprisingly, the spin splitting of these bands on Tl/Ge(111) is much smaller than on Tl/Si(111) despite the stronger surface localization and the heavier substrate. Our detailed analysis of the band structure and a tight-binding model including all relevant interactions show that a remarkable interplay between spin-orbit coupling and hybridization is responsible for this unexpected result. The comparison between the two similar hybrid systems demonstrates that the strength of the spin-orbit coupling alone, based on the atomic number of the respective elements, is not sufficient to estimate spin splittings of spin-orbit-influenced surface states.