Quantum Geometry Driven Optical Responses in 1T-MX$_2$ Monolayers: A Symmetry-Constrained Slater-Koster Tight-Binding Approach

Abstract

Centrosymmetric 1T-MX$_2$ monolayers(MLs) have attracted considerable attention owing to their intriguing transport properties and potential technological applications arising from the interplay among quantum geometry, electronic band structure, and band-gap characteristics. Despite this rich physics, a comprehensive microscopic tight-binding(TB) description that simultaneously captures these properties remains insufficiently established, while first-principles approaches can be computationally demanding for systematic investigations across different materials and perturbations. Here, we develop a transferable eleven-band Slater-Koster TB description of ML 1T-MX$_2$ TMDs and use it to establish a connection among their microscopic electronic structure, quantum geometry, and optical response. The model is constructed in an orthogonal orbital basis from the crystal geometry and symmetry-constrained SK parameters, with material-specific parametrizations obtained from DFT calculations for ML ZrS$_2$ and HfS$_2$. The resulting geometry-based Hamiltonian accurately describes the low-energy electronic structures and provides a natural framework for extending the analysis to the broader isostructural 1T-MX$_2$ family. We find that the pristine MLs possess a finite quantum metric, with the dominant contribution concentrated in the two highest occupied bands owing to the small near-gap energy separation and strong metal-chalcogen $p$-$d$ hybridization. Furthermore, we verify the interband $f$-sum rule, which directly relates the integrated optical spectral weight to the Brillouin-zone-averaged quantum metric. Our results establish optical spectral weight as an experimentally accessible probe of the quantum geometry of occupied Bloch states and provide a unified microscopic framework for connecting electronic structure, quantum geometry, and measurable optical responses across the 1T-MX$_2$ family.