Anomalous zero-field splitting for hole spin qubits in Si and Ge quantum dots

TL;DR

This paper presents an analytical model linking zero-field splitting in hole spin qubits to cubic spin-orbit interactions, revealing large effects in Si and Ge quantum dots that impact quantum processor design.

Contribution

The authors develop a new analytical model connecting zero-field splitting to cubic spin-orbit interactions, validated by numerical simulations, enhancing understanding of spin qubits in semiconductors.

Findings

Zero-field splitting can reach microelectronvolt range in Si and Ge quantum dots.

Cubic spin-orbit interactions significantly influence spin qubit behavior at zero magnetic field.

Model provides insights for optimizing spin qubits in quantum computing architectures.

Abstract

An anomalous energy splitting of spin triplet states at zero magnetic field has recently been measured in germanium quantum dots. This zero-field splitting could crucially alter the coupling between tunnel-coupled quantum dots, the basic building blocks of state-of-the-art spin-based quantum processors, with profound implications for semiconducting quantum computers. We develop an analytical model linking the zero-field splitting to spin-orbit interactions that are cubic in momentum. Such interactions naturally emerge in hole nanostructures, where they can also be tuned by external electric fields, and we find them to be particularly large in silicon and germanium, resulting in a significant zero-field splitting in the $\mu$eV range. We confirm our analytical theory by numerical simulations of different quantum dots, also including other possible sources of zero-field splitting. Our findings are applicable to a broad range of current architectures encoding spin qubits and provide a deeper understanding of these materials, paving the way towards the next generation of semiconducting quantum processors.