Transmission zero in a quantum dot with strong electron-electron interaction : Perturbative conductance calculations

A pioneering experiment [E. Schuster, E. Buks, M. Heiblum, D. Mahalu, V. Umansky, and Hadas Shtrikman, Nature 385, 417 (1997)] reported the measurement of the transmission phase of an electron traversing a quantum dot and found the intriguing feature of a sudden phase drop in the conductance valleys. Based on the Friedel sum rule for a spinless effective one-dimensional system, it has been previously argued [H.-W. Lee, Phys. Rev. Lett. 82, 2358 (1999)] that the sudden phase drop should be accompanied by the vanishing of the transmission amplitude, or transmission zero. Here we address roles of strong electron-electron interactions on the electron transport through a two-level quantum dot where one level couples with the leads much more strongly than the other level does [P. G. Silvestrov and Y. Imry, Phys. Rev. Lett. 85, 2565 (2000)]. We perform a perturbative conductance calculation with an explicit account of large charging energy and verify that the resulting conductance exhibits transmission zero, in agreement with the analysis based on the Friedel sum rule.