Parametric resonance of a two-dimensional electron gas under bichromatic irradiation

In an ultrahigh mobility 2D electron gas, even a weak nonparabolicity of the electron dispersion, by violating Kohn's theorem, can have a drastic effect on dc magnetotransport under ac drive. In this paper, 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 weak magnetic field. In particular, we find that nonparabolicity, being the simplest cause for a violation of Kohn's 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 unstable with respect to fluctuations with frequency 1/2 (omega(1)+omega(2)). The most favorable condition for this parametric instability is 1/2(omega(1)+omega(2))similar or equal toomega(c). The saturation level of this instability is also determined by the nonparabolicity. We also demonstrate that, 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, we demonstrate that, beyond a critical intensity of the two fields, the equations of motion acquire multistable solutions. As a result, the diagonal dc conductivity can assume several stable negative values at the same magnetic field.