Quantum pumping in deformable quantum dots

The charge current pumped adiabatically through an elastically deformable quantum dot suspended between electrodes is studied within the Green’s function approach. Differently from the nondeformable case, the current shows an undefined parity with respect to the pumping phase φ . The unconventional current-phase relation, analyzed in the weak pumping regime, is due to a dynamical phase shift ϕ_D caused by the elastic deformations of the central region (classical phonons). The role of the quality factor Q of the oscillator, the effects induced by a mechanical resonance and the implications for current experiments on molecular systems are also discussed.