In an ultrahigh mobility 2D electron gas, even a weak nonparabolicity of the electron dispersion, by violating Kohns theorem, can have a drastic effect on dc magnetotransport under ac drive. We study theoretically the manifestation of this effect in the dc response to the combined action of two driving ac-fields (bichromatic irradiation). Compared to the case of monochromatic irradiation, which is currently intensively studied both experimentally and theoretically, the presence of a second microwave source provides additional insight into the properties of an ac-driven 2D electron gas. In particular, we find that nonparabolicity, being the simplest cause for a violation of Kohns theorem, gives rise to new qualitative effects specific to bichromatic irradiation. Namely, when the frequencies $omega_1$ and $omega_2$ are well away from the cyclotron frequency, $omega_c$, our simple classical considerations demonstrate that the system becomes parametrically unstable with respect to fluctuations with frequency $(omega_1+omega_2)/2$. As an additional effect of nonparabolicity, this parametric instability can manifest itself in the dc properties of the system. This happens when $omega_1$, $omega_2$ and $omega_c$ are related as 3:1:2, respectively. Even for weak detuning between $omega_1$ and $omega_2$, the effect of the bichromatic irradiation on the dc response in the presence of nonparabolicity can differ dramatically from the monochromatic case. In particular, the equations of motion can acquire multistable solutions. As a result, the diagonal dc-conductivity can assume several stable negative values at the same magnetic field.
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