Strong spin-orbit interaction and $g$-factor renormalization of hole spins in Ge/Si nanowire quantum dots

TL;DR

This paper experimentally characterizes the strong and tunable spin-orbit interaction in hole spins within Ge/Si nanowire quantum dots, revealing a short spin-orbit length and significant $g$-factor enhancement, promising for quantum computing and topological states.

Contribution

The study provides the first experimental measurement of the spin-orbit length and $g$-factor renormalization in hole spins in Ge/Si nanowires, confirming theoretical predictions and highlighting their potential for quantum applications.

Findings

Spin-orbit length of ~65 nm measured in Ge/Si nanowire quantum dots.

Large magnetic field dependence of spin-mixing transition energies observed.

Significant $g$-factor enhancement with magnetic field due to strong spin-orbit interaction.

Abstract

The spin-orbit interaction lies at the heart of quantum computation with spin qubits, research on topologically non-trivial states, and various applications in spintronics. Hole spins in Ge/Si core/shell nanowires experience a spin-orbit interaction that has been predicted to be both strong and electrically tunable, making them a particularly promising platform for research in these fields. We experimentally determine the strength of spin-orbit interaction of hole spins confined to a double quantum dot in a Ge/Si nanowire by measuring spin-mixing transitions inside a regime of spin-blockaded transport. We find a remarkably short spin-orbit length of $\sim$65 nm, comparable to the quantum dot length and the interdot distance. We additionally observe a large orbital effect of the applied magnetic field on the hole states, resulting in a large magnetic field dependence of the spin-mixing transition energies. Strikingly, together with these orbital effects, the strong spin-orbit interaction causes a significant enhancement of the $g$-factor with magnetic field.The large spin-orbit interaction strength demonstrated is consistent with the predicted direct Rashba spin-orbit interaction in this material system and is expected to enable ultrafast Rabi oscillations of spin qubits and efficient qubit-qubit interactions, as well as provide a platform suitable for studying Majorana zero modes.