Inverted valley hierarchy and multifunctional properties in two-dimensional TMX 2 (TM=Ti, Zr, Hf; X=N, P, As) for flexible valleytronics

High-mobility semiconductors that simultaneously host robust valley physics and mechanical compliance are highly sought after for translating valleytronics into flexible device technologies. Using first-principles calculations, we propose monolayer TMX2 (TM = Ti, Zr, Hf; X = N, P, As) as a multifunctional 2D platform for valleytronics and flexible electronics. Crystallizing in a hexagonal P 6m2 lattice, these materials exhibit robust valley-contrasting physics, with opposite spin polarizations and inverted Berry curvatures at K/K ' valleys, and a giant conduction-band spin splitting of up to 316-375 meV in HfX2. Nitride members (ZrN2 and HfN2) achieve high room-temperature electron mobilities of ∼10 3 cm 2 V -1 s -1 , far exceeding most known 2D valleytronic materials. Mechanically, All nine monolayers feature a rare mechanical combination of a Poisson's ratio near 0.6 and low Young's moduli, affording excellent stretchability for deformable devices. Strain engineering enables continuous band-gap tuning while preserving direct-gap character, and vacuum-level alignment shows their heterostructures can realize Type I, II, and III band alignments. These properties position TM2 as a unique multifunctional 2D platform combining fast transport, intrinsic valleytronics, and mechanical compliance for flexible optoelectronic and valleytronic applications.