Origin of Indirect Optical Transitions in Few-Layer MoS₂, WS₂, and WSe₂

It has been well-established that single layer MX₂ (M = Mo, W and X = S, Se) are direct gap semiconductors with band edges coinciding at the K point in contrast to their indirect gap multilayer counterparts. In few-layer MX₂, there are two valleys along the Γ–K line with similar energy. There is little understanding on which of the two valleys forms the conduction band minimum (CBM) in this thickness regime. We investigate the conduction band valley structure in few-layer MX₂ by examining the temperature-dependent shift of indirect exciton photoluminescence peak. Highly anisotropic thermal expansion of the lattice and the corresponding evolution of the band structure result in a distinct peak shift for indirect transitions involving the K and Λ (midpoint along Γ-K) valleys. We identify the origin of the indirect emission and concurrently determine the relative energy of these valleys