I investigate the time-dependent transport through a quantum wire with an impurity in the presence of finite range electron-electron interactions within the Luttinger liquid description [1,2,3]. I discuss the influence of the spatial shape of the ac electric field onto transport properties of the system and find that the scaling behavior of the occupation probability of the sidebands depends on the spatial range of the voltage drop. I observe a cross-over between the Tien-Gordon scaling [4] of the sidebands and a regime in which the scaling reflects the ranges of both, the electron-electron interaction and the electric field. Moreover, for intermediate interaction strengths, the nonlinear differential conductance shows cusp like periodic minima, with a similar activation mechanism as the one predicted for fractional quantum Hall edge states [5]. These mode lockings are here due to the finite nonzero range of the interaction and are independent of the shape of the driving electric field.

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[2] G. Cuniberti et al. AC-conductance of quantum wire with electron-electron interaction. Phys. Rev. B 56, 1515 (1998).
[3] G. Cuniberti et al. Frequency scaling of photo- induced tunneling. To appear in Europhys. Lett. (1999).
[4] P.K. Tien, and J.P. Gordon. Multiphoton process observed in the interaction of microwave fields with the tunneling between superconductor films. Phys. Rev. B 129, 647 (1963).
[5] H.H. Lin, and M.P.A. Fisher. Mode locking in quantum Hall effect point contacts Phys. Rev. B 54, 10593 (1996-I).