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Focusing on electron transport through a periodically driven resonant tunneling diode, we study the generation of a non-vanishing dc-current by applying symmetry breaking external ac fields with phase difference φ in a statically unbiased system. The effect of an environment is investigated using the system-bath Hamiltonian represented by the electron system coupled to harmonic oscillator modes with a Drude–Lorentz spectral density. To carry out simulations, we use the hierarchal equations of motion approach in the Wigner representation including a self-consistently constructed electric field that is determined from the electron distribution using the Poisson equation. We show that the maximal pumping current at a phase difference near φ = π/2 is strongly influenced by the system-bath coupling strength. The effect of dissipation is diminished if the self-consistent part of the potential is ignored.

Electron Pumping under Non-Markovian Dissipation: The Role of the Self-Consistent Field