Isospin phases of vertically coupled double quantum rings under the influence of perpendicular magnetic fields

TL;DR

This study investigates the electronic structure and isospin phases of vertically coupled double quantum rings under perpendicular magnetic fields using density functional theory, revealing how coupling strength influences spectral features and electron configurations.

Contribution

It provides a detailed analysis of how inter-ring coupling and magnetic fields affect the electronic states and isospin phases in double quantum rings, a topic not extensively explored before.

Findings

Strong coupling leads to spectra similar to single quantum rings.

Magnetic fields cause spectral flattening but still allow identification of shell structures.

Weak coupling exhibits isospin oscillations as a function of magnetic field.

Abstract

Vertically coupled double quantum rings submitted to a perpendicular magnetic field $B$ are addressed within the local spin-density functional theory. We describe the structure of quantum ring molecules containing up to 40 electrons considering different inter-ring distances and intensities of the applied magnetic field. When the rings are quantum mechanically strongly coupled, only bonding states are occupied and the addition spectrum of the artificial molecules resembles that of a single quantum ring, with some small differences appearing as an effect of the magnetic field. Despite the latter has the tendency to flatten the spectra, in the strong coupling limit some clear peaks are still found even when $B\neq 0$ that can be interpretated from the single-particle energy levels analogously as at zero applied field, namely in terms of closed-shell and Hund's-rule configurations. Increasing the inter-ring distance, the occupation of the first antibonding orbitals washes out such structures and the addition spectra become flatter and irregular. In the weak coupling regime, numerous isospin oscillations are found as a function of $B$.