Spin Structure of K Valleys in Single-Layer WS_{2} on Au(111)

The spin structure of the valence and conduction bands at the K[over ¯] and K[over ¯]^{'} valleys of single-layer 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 K[over ¯] and the K[over ¯]^{'} 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).