A quantum engine by pumping electrons in a nanojunction with a single gate and dynamic tunnel couplings to the leads

We configure a nanojunction to function as a quantum engine by making the tunnel couplings between the channel and the leads dynamic and applying a time-dependent gate potential. The individual dynamics of each of the couplings to the leads as well as the gate potential are then made to follow an operating protocol so that electrons are pumped from the left lead, through the channel, and on to the right lead. We express the electron energy current flowing across the device in terms of nonequilibrium Green's functions. Using the Keldysh formalism, we then express these nonequilibrium Green's functions in terms of steady-state Green's functions. The steady-state Green's functions, in turn, are expressed in terms of the equilibrium Green's functions of the free leads. Equilibrium Green's functions are determined from the equation of motion of each free lead.