Geometry-Induced Spin Filtering in Photoemission Maps from ${\mathrm{WTe}}_2$ Surface States

We demonstrate that an important quantum material ${\mathrm{WTe}}_2$ exhibits a new type of geometry-induced spin filtering effect in photoemission, stemming from low symmetry that is responsible for its exotic transport properties. Through the laser-driven spin-polarized angle-resolved photoemission Fermi surface mapping, we showcase highly asymmetric spin textures of electrons photoemitted from the surface states of ${\mathrm{WTe}}_2$. Such asymmetries are not present in the initial state spin textures, which are bound by the time-reversal and crystal lattice mirror plane symmetries. The findings are reproduced qualitatively by theoretical modeling within the one-step model photoemission formalism. The effect could be understood within the free-electron final state model as an interference due to emission from different atomic sites. The observed effect is a manifestation of time-reversal symmetry breaking of the initial state in the photoemission process, and as such it cannot be eliminated, but only its magnitude influenced, by special experimental geometries.

Figure 1

(a),(b) Spin-integrated laser ARPES Fermi surface maps measured with $p$- and $s$-polarized light. (c),(d) Corresponding energy dispersions $E(k_x)$ for $k_y=0$ as indicated by the dashed lines in (a) and (b). (e),(f) Experimental laser-SARPES $57\times 89\mathrm{pixel}$ Fermi surface maps taken at two nearby spots on the same cleave. The false color scale refers to the spin polarization $S_{fy}$ in the ensemble of the photoemitted electrons. (g) Schematic geometry of the SARPES experiment. The maps were measured using the lens deflector system collecting the emission angles indicated by the yellow cone with the sample rotated by $\theta =25°$ with respect to the lens axis using $p$-polarized light and probing the spin along the $y$ axis, as defined in (g).

Figure 2

Crystal geometry and initial state spin textures. (a) The 3D impression of the ${\mathrm{WTe}}_2$ crystal structure. (b) The probed surface with two possible terminations, which we label $D1$ and $D2$. (c) The $S_y$ component of the theoretical Fermi level spin texture, which is the same for both domains. The size of the symbols corresponds to the spin polarization in the first layer (containing two formula units). (d) The surface state charge density in real space at $k_x=-0.3{\AA }^{-1}$ and initial energy $-25\mathrm{meV}$ (see Supplemental Material Fig. S6 [26]).

Figure 3

One-step model calculation of spin polarization $S_y$ (a)–(d) $p$-polarized and (e)–(h) $s$-polarized light. (a),(c),(e),(g) Pure spin polarization. (b),(d),(f),(h) Weighted by photoemission intensity. (a),(b),(e),(f) FEFS was used. (c),(d),(g),(h) The TR-LEED final state was used. (i)–(k) The magnitude of $S_y$ at 3-momenta $S1–S3$ indicated in (b); solid lines are for $p$-polarized light and dashed lines are for $s$-polarized light. (i),(j) The dependence on photon energy for the FEFS and TR-LEED final states, respectively. (k) The dependence on the off-normal light incidence angle. (l) The dependence on binding energy for the momenta indicated in (m), where TR-LEED maps (with $p$-polarized light) at several binding energies are shown. For convenience, the dashed lines in (a), (c), (e), and (g) indicate the location of the surface state.