  We describe nonlinear phonon-thermoelectric devices where charge current and
electronic and phononic heat currents are coupled, driven by voltage and
temperature biases, when phonon-assisted inelastic processes dominate the
transport. Our thermoelectric transistors and rectifiers can be realized in a
gate-tunable double quantum-dot system embedded in a nanowire which is
realizable within current technology. The inelastic electron-phonon scattering
processes are found to induce pronounced charge, heat, and cross rectification
effects, as well as a thermal transistor effect that, remarkably, can appear in
the present model even in the linear-response regime without relying on
negative differential thermal conductance.
