Quantum theory of plasmon-phonon scattering in multisubband systems

We present a first-principles quantum theory of a critical yet unexplored energy-loss pathway in low-dimensional semiconductors: resonant second-order scattering between multisubband plasmons mediated by longitudinal optical phonons. Specifically, we demonstrate how a high-energy multisubband plasmon decays into a lower-energy plasmon state via phonon emission - a fundamental process governing energy relaxation and decoherence in quantum wells. Through exact diagonalization of the coupled plasmon-phonon system and derivation of an effective Hamiltonian, we identify density-tunable resonance conditions that maximize scattering efficiency. Our numerical simulations for GaInAs quantum wells reveal scattering rates (~10 ns -1 ) competitive with radiative losses, with carrier density acting as a control knob. These results resolve the interplay of collective electronic and vibrational modes in confined systems, providing design principles to mitigate losses in infrared photodetectors, quantum cascade lasers, and plasmon-based quantum devices.