Current-driven plasmons in two-layer semiconductor heterostructures: Long-wavelength features and two-stream instability

In this work, the plasmonic oscillations in two-dimensional charge-coupled semiconductor layers, including those biased by an external current, have been thoroughly investigated by the hydrodynamic model. The relative amplitudes of the charge-density oscillations and their phase shift in the two coupled layers have been calculated. For the long wavelengths important in experimental studies, it has been found that the electron relaxation radically modifies the mode types and dispersion, providing linear portions of the wave-vector dependencies followed by a square root branching. We have shown that the hydrodynamic approach does not predict any instability for drifting electrons in two coupled identical layers, while plasmonic instability is possible for the layers with distinct characteristics. For these cases, there exists a narrow <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>(</a:mo><a:mi>ω</a:mi><a:mo>,</a:mo><a:mi>k</a:mi><a:mo>)</a:mo></a:mrow></a:math> region with strong (resonant) interlayer interaction, where the real parts of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>ω</b:mi><b:mo>(</b:mo><b:mi>k</b:mi><b:mo>)</b:mo></b:mrow></b:math> of the plasmon modes are identical and linear in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>k</c:mi></c:math> (a second linear portion). The imaginary parts are different and one of them can change sign, leading to the plasmonic instability effect. This instability develops as the two-stream convective instability, whose threshold and frequency critically depend on the velocity of drifting electrons. Under negligibly weak electron relaxation, there is no drift velocity threshold for the revealed instability, while electron relaxation originates the finite velocity threshold. The numerical estimations of the instability critical parameters are provided for the GaAs-based heterostructures. We suggest that this investigation of charge-coupled current-biased semiconductor layers brings the new knowledge to solid-state plasmonic physics and can be used in the practical search of terahertz electric instabilities and sources of terahertz emission.