An Approximate Sign Sum Rule for the Transmission Amplitude Through a Quantum Dot

TL;DR

This paper investigates the phase behavior of electron transmission through a disordered quantum dot, revealing a near-sum rule over a resonance cycle and uncovering interaction-induced phase correlations.

Contribution

It introduces an approximate sign sum rule for the transmission phase and analyzes disorder effects and phase correlations in quantum dots.

Findings

Total phase change over a resonance cycle is approximately zero (mod 2π).

Deviations from the sum rule are small when level spacing is comparable to charging energy.

Disorder-averaged phase correlations indicate interaction effects between different gate voltages.

Abstract

We study the phase of the transmission amplitude through a disordered quantum dot in the Coulomb blockade regime. We calculate the phase dependence on gate voltage for a disorder configuration. We show that over a ``period'', consisting of a resonance and a transmission valley, the total phase change is 0 (mod $2\pi$). Deviations from this sum rule are small in the parameter (level spacing/charging energy). The disorder-averaged phase-phase correlation function is found showing interaction-induced correlations between phases at different gate voltages.