Amplitudes of Hall field-induced resistance oscillations with a two-harmonic density of states

We derive explicit strong-field asymptotics for the normalized differential resistance in Hall field-induced resistance oscillations (HIRO) within the Vavilov-Aleiner-Glazman kinetic framework. For a single-harmonic density of states, the leading oscillation amplitude is set by the full backscattering rate $1/\tau(\pi)$. Extending the theory to a two-harmonic density of states, we show that the off-diagonal mixed kernel $\gamma_{12}$ admits an exact single-integral representation, from which the strong-field asymptotics follow directly. The resulting odd harmonics, notably $m=1$ and $m=3$, have coefficients determined by combinations of $1/\tau(0)$ and $1/\tau(\pi)$, while the leading $m=2$ amplitude remains unchanged. On exact-kernel mock data generated and fit within the same model, with $\tau_{\rm tr}$ and $\tau_{\rm in}$ held fixed, the resulting extraction protocol recovers $\tau_q$, $\tau(\pi)$, and -- when the $m=1,3$ harmonics are resolved -- $\tau(0)$ to sub-percent accuracy, with $\tau(0)$ providing a consistency check on the disorder description.