Emergent Quantum Phenomena of a Noncentrosymmetric Charge Density Wave in 1T -Transition Metal Dichalcogenides

$1T$-transition metal dichalcogenides (TMDs) have been an exciting platform for exploring the intertwinement of charge density waves and strong correlation phenomena. While the David star structure has been conventionally considered as the underlying charge order in the literature, recent scanning tunneling probe experiments on several monolayer $1T$-TMD materials have motivated a new, alternative structure, namely, the anion-centered David star structure. In this Letter, we show that this novel anion-centered David star structure manifestly breaks inversion symmetry, resulting in flat bands with pronounced Rashba spin-orbit couplings. These distinctive features unlock novel possibilities and functionalities for $1T$-TMDs, including the giant spin Hall effect, the emergence of Chern bands, and spin liquid that spontaneously breaks crystalline rotational symmetry. Our findings establish promising avenues for exploring emerging quantum phenomena of monolayer $1T$-TMDs with this novel noncentrosymmetric structure.