Theory of Silicon Spin Qubit Relaxation in a Synthetic Spin-Orbit Field

TL;DR

This paper develops a theoretical model for silicon spin qubit relaxation influenced by magnetic field gradients, accounting for interface roughness, and matches experimental data while exploring how gradients affect qubit control frequencies.

Contribution

It introduces a valley-dependent envelope function theory to analyze the impact of interface roughness and magnetic gradients on silicon spin qubit relaxation and control.

Findings

The model quantitatively matches experimental relaxation measurements.

Magnetic field gradients can alter the EDSR Rabi frequency depending on interface roughness.

Adding a micromagnet can sometimes reduce the EDSR frequency in ideal interfaces.

Abstract

We develop the theory of single-electron silicon spin qubit relaxation in the presence of a magnetic field gradient. Such field gradients are routinely generated by on-chip micromagnets to allow for electrically controlled quantum gates on spin qubits. We build on a valley-dependent envelope function theory that enables the analysis of the electron wave function in a silicon quantum dot with an arbitrary roughness at the interface. We assume the presence of single-layer atomic steps at a Si/SiGe interface and study how the presence of a gradient field modifies the spin-mixing mechanisms. We show that our theoretical modeling can quantitatively reproduce results of experimental measurements of qubit relaxation in silicon in the presence of a micromagnet. We further study in detail how a field gradient can modify the EDSR Rabi frequency of a silicon spin qubit. While this strongly depends on the details of the interface roughness, interestingly, we find that adding a micromagnet on top of a spin qubit with an ideal interface can even reduce the EDSR frequency within some interval of the external magnetic field strength.