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Transmission zero in a semichaotic quantum dot with strong electron-electron interaction

The pioneering experiment [Nature 385, 417 (1997)] reported the measurement of the transmission phase of the electron traversing a quantum dot and found the intriguing feature of the sudden phase drop in conductance valleys. Based on the Friedel sum rule for a spinless effective one-dimensional system, it has been previously argued [Phys. Rev. Lett. 82, 2358 (1999)] that the sudden phase drop should be accompanied by the vanishing of the transmission amplitude, or the transmission zero. Here we address roles of strong electron-electron interaction on the electron transport through a semichaotic dot, where the widths of single-particle levels in the dot can differ from each other by orders of magnitude [Phys. Rev. Let. 85, 2565 (2000)]. We perform a perturbative conductance calculation with the explicit account of the large charging energy and verify that the resulting conductance exhibits the transmission zero, in agreement with the analysis based on the Friedel sum rule.