Fig. 3.

Origin for Zeeman splitting in bilayer. a Single-particle energy states at ±K-points of bilayer TMD at zero magnetic field and in presence of interlayer hopping t _⊥. The spin–valley-layer locking results in optical selection rules such that in both valleys, the spin degree of freedom is locked to the emission helicity. b Schematic diagram of the Zeeman splitting in bilayer MoTe₂ under positive magnetic field at ±K-points. Red (blue) transition indicates the PL emission with photon energy E ₊ (E ₋) and circular polarization σ ₊ (σ ₋). The upper and the lower layer in the same valley have opposite spin. Green and gray arrows show the magnetic moment contributions of the spin and atomic orbital to the Zeeman splitting, respectively. In the presence of a positive magnetic field, the spin contributions cancel, whereas the intracellular or atomic orbital contribution leads to E ₊ < E ₋ in both the valleys