Time-dependent quantum transport far from equilibrium: An exact nonlinear response theory

In this work, we present a theory to calculate the time-dependent current flowing through an arbitrary noninteracting nanoscale phase-coherent device connected to arbitrary noninteracting external leads, in response to sharp step- and square-shaped voltage pulses. Our analysis is based on the Keldysh nonequilibrium Green's-functions formalism, and provides an exact analytical solution to the transport equations in the far from equilibrium, nonlinear response regime. However, the essential feature of our solution is that it does not rely on the commonly used wideband approximation where the coupling between device scattering region and leads is taken to be independent of energy, and as such provides a way to perform transient transport calculations from first principles on realistic systems, taking into account the detailed electronic structure of the device scattering region and the leads. We then perform a model calculation for a quantum dot with Lorentzian linewidth and show how interesting finite-bandwidth effects arise in the time-dependent current dynamics.