Friedel phase discontinuity and bound states in the continuum in quantum dot systems

TL;DR

This paper investigates the Friedel phase behavior in quantum dot systems with bound states in the continuum, revealing abrupt phase jumps and charge changes linked to conductance discontinuities.

Contribution

It demonstrates the connection between Friedel phase jumps, BICs, and conductance discontinuities in quantum dot systems, extending previous theoretical insights.

Findings

Friedel phase exhibits abrupt jumps at BIC energies.

Charge changes discontinuously when BIC energy crosses the Fermi level.

Conductance shows predicted discontinuities related to BIC behavior.

Abstract

n this article we study the Friedel phase of the electron transport in two different systems of quantum dots which exhibit bound states in the continuum (BIC). The Friedel phase jumps abruptly in the energies of the BICs, which is associated to the vanishing width of these states, as shown by Friedrich and Wintgen in Phys. Rev. A \textbf{31}, 3964 (1985). This odd behavior of the Friedel phase has consequences in the charge through the Friedel sum rule. Namely, if the energy of the BIC drops under the Fermi energy the charge changes abruptly in a unity. We show that this behavior closely relates with discontinuities in the conductance predicted for interacting quantum dot systems.