The non-equilibrium transport of electrons confined at an atomically sharp interface and subject to a periodic potential is studied. We find a pronounced negative differential resistance, the magnitude of which increases with increasing modulation strength. The data is qualitatively consistent with the Esaki–Tsu transport model. We emphasize the significance of the two-dimensionality of the electron system and the gate to inhibit domain formation. Additional features in the source–drain current are attributed to Bloch-phonon resonances.