Selective Probing of Hidden Spin-Polarized States in Inversion-Symmetric Bulk ${\mathrm{MoS}}_2$

Spin- and angle-resolved photoemission spectroscopy is used to reveal that a large spin polarization is observable in the bulk centrosymmetric transition metal dichalcogenide ${\mathrm{MoS}}_2$. It is found that the measured spin polarization can be reversed by changing the handedness of incident circularly polarized light. Calculations based on a three-step model of photoemission show that the valley and layer-locked spin-polarized electronic states can be selectively addressed by circularly polarized light, therefore providing a novel route to probe these hidden spin-polarized states in inversion-symmetric systems as predicted by Zhang et al. [Nat. Phys. 10, 387 (2014).].

Figure 1

(a) Structural model (top) and Brillouin zone (bottom) of $2H\text{−}{\mathrm{MoS}}_2$. (b) ARPES intensity map along $\overline{K}-\overline{\mathrm{\Gamma }}$ direction (top), and DFT-LDA calculated band structure showing the band dispersion along $K-\mathrm{\Gamma }$ and $H-K$ directions (bottom). (c)–(d) Spin-resolved intensities (top) and spin polarization curves (bottom) at the $\overline{K}$ point along $x$, $y$, and $z$, respectively. Continuous red lines in the bottom panels are Gaussian fits, resulting in $P_x=\mp 0.08$, $P_y=\pm 0.05$, and $P_z=\mp 0.28$. Spin-ARPES data were acquired at $h\nu =50\mathrm{eV}$ with $s$-polarized light.

Figure 2

Spin-ARPES data acquired at $h\nu =50$ and $h\nu =58\mathrm{eV}$. (a)–(c) Spin-resolved intensities (top) and spin polarization curves (bottom) along $z$ at the $\overline{K}$ point acquired with $p$, $C_L$, and $C_R$ polarization, respectively ($h\nu =50\mathrm{eV}$). (d),(e) Spin-resolved intensities (top) and spin polarization curves (bottom) at the $\overline{K}$ point acquired with $C_L$ and $C_R$ polarization, and $h\nu =58\mathrm{eV}$. Continuous red lines in the bottom panels are Gaussian fits, resulting in $P_z(p,50\mathrm{eV})=\mp 0.50$, $P_z(C_L,50\mathrm{eV})=\mp 0.68$, $P_z(C_R,50\mathrm{eV})=\pm 0.85$, $P_z(C_L,58\mathrm{eV})=\mp 0.54$, and $P_z(C_R,58\mathrm{eV})=\pm 0.91$.

Figure 3

(a) Schematic of the layer-resolved band dispersion of VB1 and VB2 around the $K$ point. (b) Dipole-allowed transitions for the eigenstate of VB1 for vanishing interlayer coupling ($\alpha =0$) at the $K$ point.

Figure 4

Three-step model photoemission calculations. (a)–(d) Spin polarization ($P_z$) maps for $p$, $s$, $C_L$, and $C_R$ polarization, respectively ($h\nu =50\mathrm{eV}$). (e) Experimental and simulated spin polarization along $z$. (f)–(h) radial integral ($\rho$), photon energy ($h\nu$) and IMFP (${\lambda }_e$) dependence of $P_z$, respectively. Empty symbols in (g) show the experimental $P_z$ from Fig. 2. (i)–(n) Spin-resolved intensity maps for $C_L$ (top panels) and $C_R$ (bottom panels) polarized light.