The spin structure of the valence and conduction bands at the $\overline{K}$ and ${\overline{K}}^{\prime }$ valleys of single-layer ${\mathrm{WS}}_2$ on Au(111) is determined by spin- and angle-resolved photoemission and inverse photoemission. The bands confining the direct band gap of 1.98 eV are out-of-plane spin polarized with spin-dependent energy splittings of 417 meV in the valence band and 16 meV in the conduction band. The sequence of the spin-split bands is the same in the valence and in the conduction bands and opposite at the $\overline{K}$ and the ${\overline{K}}^{\prime }$ high-symmetry points. The first observation explains “dark” excitons discussed in optical experiments; the latter points to coupled spin and valley physics in electron transport. The experimentally observed band dispersions are discussed along with band structure calculations for a freestanding single layer and for a single layer on Au(111).

• Received 21 June 2018
• Revised 19 July 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.136402