Classification and magic magnetic-field directions for spin-orbit-coupled double quantum dots

TL;DR

This paper classifies spin-orbit-coupled double quantum dots into six classes based on their $g$-tensor properties, revealing how magnetic field directions influence qubit behavior and simplifying spin physics at 'magic directions' for quantum computing.

Contribution

It introduces a classification scheme for double quantum dots based on $g$-tensor analysis, linking physical characteristics to magnetic field directions and identifying 'magic directions' that simplify spin dynamics.

Findings

Six classes of double quantum dots determined by $g$-tensor partitioning.

Identification of 'magic directions' where spin physics simplifies.

Analysis of 'magic loops' with equal local Zeeman splittings.

Abstract

The spin of a single electron confined in a semiconductor quantum dot is a natural qubit candidate. Fundamental building blocks of spin-based quantum computing have been demonstrated in double quantum dots with significant spin-orbit coupling. Here, we show that spin-orbit-coupled double quantum dots can be categorised in six classes, according to a partitioning of the multi-dimensional space of their $g$-tensors. The class determines physical characteristics of the double dot, i.e., features in transport, spectroscopy and coherence measurements, as well as qubit control, shuttling, and readout experiments. In particular, we predict that the spin physics is highly simplified due to pseudospin conservation, whenever the external magnetic field is pointing to special directions (`magic directions'), where the number of special directions is determined by the class. We also analyze the existence and relevance of magic loops in the space of magnetic-field directions, corresponding to equal local Zeeman splittings. These results present an important step toward precise interpretation and efficient design of spin-based quantum computing experiments in materials with strong spin-orbit coupling.