Probing sliding ferroelectricity in bilayer T$_\mathrm{d}$-WTe$_2$ with high-harmonic generation

High-harmonic generation is a sensitive all-optical probe of symmetry and electron dynamics in solids. Here, we use first-principles time-dependent density functional theory (TDDFT) to study high-harmonic generation in T$_d$-WTe$_2$, a two-dimensional semimetal with switchable out-of-plane ferroelectric polarization driven by interlayer sliding. We show that the mirror-symmetry breaking underlying the ferroelectric state produces robust signatures in polarization-resolved high-harmonic spectra, enabling optical identification of the polarization state. By incorporating interlayer shear motion in coupled electron-lattice TDDFT simulations, we further show that the 0.24 THz shear mode is slow enough to remain effectively decoupled from the ultrafast electronic response responsible for harmonic emission. Our results establish high-harmonic spectroscopy as a non-invasive probe of sliding ferroelectricity and lattice symmetry in two-dimensional quantum materials.