Finite-momentum superconductivity from chiral bands in twisted MoTe$_2$

A recent experiment has reported unconventional superconductivity in twisted bilayer MoTe$_2$, emerging from a normal state that exhibits a finite anomalous Hall effect -- a signature of intrinsic chirality. Motivated by this discovery, we construct a continuum model for twisted MoTe$_2$ constrained by lattice symmetries from first-principles calculations that captures the moir\'{e}-induced inversion symmetry breaking even in the absence of a displacement field. Building on this model, we show that repulsive interactions give rise to finite-momentum superconductivity via the Kohn-Luttinger mechanism in this chiral moir\'{e} system. Remarkably, the finite-momentum superconducting state can arise solely from internal symmetry breaking of the moir\'{e} superlattice, differentiating it from previously studied cases that require external fields. It further features a nonreciprocal quasiparticle dispersion and an intrinsic superconducting diode effect. Our results highlight a novel route to unconventional superconducting states in twisted transition metal dichalcogenides moir\'{e} systems, driven entirely by intrinsic symmetry-breaking effects.