  Two electrons in a quantum dot repel each other: their interaction can be
characterized by a positive interaction energy. From the theory of
superconductivity, we also know that mechanical vibrations of the crystal
lattice can make the electron-electron interaction attractive. Analogously, if
a quantum dot interacts with a mechanical degree of freedom, the effective
interaction energy can be negative; that is, the electron-electron interaction
might be attractive. In this work, we propose and theoretically study an
engineered electromechanical system that exhibits electron-electron attraction:
a quantum dot suspended on a nonlinear mechanical resonator, tuned by a bottom
and a top gate electrode. We focus on the example of a dot embedded in a
suspended graphene ribbon, for which we identify conditions for
electron-electron attraction. Our results suggest the possibility of electronic
transport via tunneling of packets of multiple electrons in such devices,
similar to that in superconducting nanostructures, but without the use of any
superconducting elements.
