Title: Quantized Acoustoelectric Floquet Effect in Quantum Nanowires

Abstract: External coherent fields can drive quantum materials into non-equilibrium states, revealing exotic properties that are unattainable under equilibrium conditions -- an approach known as ``Floquet engineering.'' While optical lasers have commonly been used as the driving fields, recent advancements have introduced nontraditional sources, such as coherent phonon drives. Building on this progress, we demonstrate that driving a metallic quantum nanowire with a coherent wave of terahertz phonons can induce an electronic steady state characterized by a persistent quantized current along the wire. The quantization of the current is achieved due to the coupling of electrons to the nanowire's vibrational modes, providing the low-temperature heat bath and energy relaxation mechanisms. Our findings underscore the potential of using non-optical drives, such as coherent phonon sources, to induce non-equilibrium phenomena in materials. Furthermore, our approach suggests a new method for the high-precision detection of coherent phonon oscillations via transport measurements.