Synchronic scattering and geometric dephasing in microwave-induced resistance oscillations

We present a novel quantum transport model for microwave-induced resistance oscillations (MIRO) where we prove that the instantaneous scattering rate is directly modulated by the velocity of the driven coherent state. This interaction peaks exactly at $\omega t = 2n\pi$, where the wave packets sweep through the impurity landscape at maximum speed, breaking time-reversal symmetry to generate a net direct current. Additionally, we introduce a dephasing architecture to explain amplitude saturation: a non-linear geometric dephasing ($\exp(-A/R_c)$) triggered when the displacement amplitude $A$ of the oscillating coherent state, approaches the cyclotron radius $R_{c}$. This perfectly captures the linear-to-sublinear power crossover at high intensities, offering a fully coherent description of non-equilibrium transport.