Energy spectra of three electrons in Si/SiGe single and vertically coupled double quantum dots

TL;DR

This paper investigates the energy spectra of three electrons in Si/SiGe quantum dots, considering effects like spin-orbit coupling and valley interactions, and explores how magnetic fields and dot parameters influence ground states and degeneracies.

Contribution

It provides a comprehensive analysis of three-electron energy spectra in Si/SiGe quantum dots, including effects like valley coupling and spin-orbit interaction, with experimental validation and phase diagrams.

Findings

Ground state configurations depend on dot size and valley splitting.

Magnetic field can switch ground states between doublet and quartet.

Anticrossings due to spin-orbit coupling facilitate spin manipulation.

Abstract

We study three-electron energy spectra in Si/SiGe single and vertically coupled double quantum dots where all the relevant effects, such as, the Zeeman splitting, spin-orbit coupling, valley coupling and electron-electron Coulomb interaction are explicitly included. In the absence of magnetic field, our results in single quantum dots agree well with the experiment by Borselli {\em et al.} [Appl. Phys. Lett. {\bf 98}, 123118 (2011)]. We identify the spin and valley configurations of the ground state in the experimental cases and give a complete phase-diagram-like picture of the ground state configuration with respect to the dot size and valley splitting. We also explicitly investigate the three-electron energy spectra of the pure and mixed valley configurations with magnetic fields in both Faraday and Voigt configurations. We find that the ground state can be switched between doublet and quartet by tuning the magnetic field and/or dot size. The three-electron energy spectra present many anticrossing points between different spin states due to the spin-orbit coupling, which are expected to benefit the spin manipulation. We show that the negligibly small intervalley Coulomb interaction can result in magnetic-field independent quartet-doublet degeneracy in the three-electron energy spectrum of the mixed valley configuration. Furthermore, we study the barrier-width and barrier-height dependences in vertically coupled double quantum dots with both pure and mixed valley configurations. Similar to the single quantum dot case, anticrossing behavior and quartet-doublet degeneracy are observed.