Interactions and Broken Time-Reversal Symmetry in Chaotic Quantum Dots

TL;DR

This paper investigates how broken time-reversal symmetry affects interactions in chaotic quantum dots, showing that neglecting Cooper channel effects in spin density functional theory leads to discrepancies with RPA-like approaches.

Contribution

It demonstrates that breaking time-reversal symmetry improves agreement between RPA-like and spin density functional methods in quantum dot interaction calculations.

Findings

Good agreement between RPA-like and spin density functional results when time-reversal symmetry is broken.

Discrepancies in symmetric cases are due to neglect of Cooper channel effects.

Higher-order interaction terms are crucial for accurate modeling of quantum dots.

Abstract

When treating interactions in quantum dots within a RPA-like approach, time-reversal symmetry plays an important role as higher-order terms -- the Cooper series -- need to be included when this symmetry is present. Here we consider model quantum dots in a magnetic field weak enough to leave the dynamics of the dot chaotic, but strong enough to break time-reversal symmetry. The ground state spin and addition energy for dots containing 120 to 200 electrons are found using local spin density functional theory, and we compare the corresponding distributions with those derived from an RPA-like treatment of the interactions. The agreement between the two approaches is very good, significantly better than for analogous calculations in the presence of time-reversal symmetry. This demonstrates that the discrepancies between the two approaches in the time-reversal symmetric case indeed originate from the Cooper channel, indicating that these higher-order terms might not be properly taken into account in the spin density functional calculations.