Configuration-dependent electronic and optical properties of 2D Mo$_{1-x}$W$_x$S$_2$ alloys across the full composition range

Abstract

Here we analyze multiple symmetry-inequivalent atomic configurations across the entire composition range of the isovalent and isostructural Mo$_x$W$_{1-x}$S$_2$ alloy using density-functional theory and Monte Carlo simulations. Our results show that although structural stability and energetics are largely composition-driven, the electronic and optical properties exhibit configuration dependence, with local atomic arrangements critically shaping band-edge splitting, valley structure, effective-mass anisotropy, and optical selection rules. In contrast to the pristine monolayers, even in the absence of spin-orbit coupling (SOC), splitting of the band edges at the $K$ point is observed across the entire composition range. In particular, while the valence-band maximum (VBM) remains largely robust, the conduction-band minimum (CBM) shows strong configuration-dependent splitting from few meV up to hundredths of meV. This behaviour leads to a non-trivial dependence of the valley energetics. Configurations with well-separated conduction bands support additional optically active transitions beyond the conventional A and B excitons in MoS$_2$ and WS$_2$ monolayers, whereas nearly degenerate cases exhibit a reduced number of allowed transitions, observed for specific configurations at $x = 1/3$ and $x = 2/3$. These results demonstrate that the number and character of optically active transitions are governed not only by composition, but also by the microscopic arrangement of atoms. Moreover, we found the hole effective masses at the VBM show configuration-dependent anisotropy, reflecting sensitivity to local symmetry breaking and implying direction-dependent transport.