The steady-state cooling of a nanomechanical resonator interacting with three coupled quantum dots is studied. General conditions for the cooling to the ground state with single- and two-electron dark states are obtained. The results show that in the case of the interaction of the resonator with a single-electron dark state, no cooling of the resonator occurs unless the quantum dots are not identical. The steady-state cooling is possible only if the energy state of the quantum dot coupled to the drain electrode is detuned from the energy states of the dots coupled to the electron source electr...
