Figure 4: Layer-dependent spin-valley coupled Q valleys in TMDCs.

(a) Calculated band structure of 3L MoS₂. The bottom of conduction band is located at the Q (Q’) valleys. At the edge of each Q (Q’) valley, the Fermi level only crosses the lowest non-degenerate sub-band, whose spin-up and spin-down sub-bands are lifted by 4.3 meV. (b) Calculated band structure of 6L WS₂. The energy bands are spin-degenerate at the edge of each Q (Q’) valley. These spin-valley coupled band edges are further illustrated in (c), where the red and blue colours denote the spin-down and spin-up bands, respectively. Q₁, Q₂ and Q₃ have the same spin, and Q₁’, Q₂’ and Q₃’ are their time reversals. (d) Schematic diagrams for the Bloch bands, showing the valley Zeeman effect in odd-layer devices and the spin Zeeman effect in even-layer devices. For odd-layer samples, the sub-band at Fermi level is non-degenerate at B=0; at relatively high magnetic field, the degeneracy between Q and Q’ valleys is further lifted by the valley Zeeman effect. It follows that an LL sextet can be lifted into two LL triplets caused by the valley Zeeman effect. For even-layer samples, the sub-band at Fermi level is spin-degenerate at B=0; at relatively high magnetic field, the degeneracy between up and down spins is lifted by the spin Zeeman effect. It follows that an LL duodectets can be lifted into LL sextets caused by the spin Zeeman effect.