Singlet-triplet oscillations in multivalley Si double quantum dots

TL;DR

This paper provides a theoretical analysis of singlet-triplet oscillations in silicon double quantum dots, focusing on valley effects, spin-valley coupling, and comparison with experimental data to understand valley-dependent properties.

Contribution

It introduces a detailed theoretical model of charge separation and singlet-triplet mixing in Si quantum dots, accounting for valley occupation patterns and spin-valley resonances, supported by experimental comparisons.

Findings

Strong renormalization of oscillation frequency near spin-valley resonances.

Valley occupation patterns influence g-factor variations.

Electric field noise affects dephasing near spin-valley resonances.

Abstract

Charge separation from the $(4,0)$ to the $(3,1)$ state in a Si/SiGe double quantum dot is commonly used for initialization of spin qubits and Pauli-spin-blockade readout. It was used in recent experiments involving creation of the $(3,1)$ singlet, and subsequent shuttling of one of the electrons. We present a theoretical description of the process of charge separation and singlet-triplet mixing, arriving at expressions for the singlet return probability that take into account experimentally observed finite probabilities of the creation of singlets with various patterns of valley occupations. In our analysis we focus on magnetic fields for which the electron spin Zeeman splitting is close to the valley splitting in one of the dots, when the spin-valley coupling causes a strong renormalization of the frequency of oscillations of singlet return probability. The latter effect has been recently used to perform valley splitting mapping by shuttling of one quantum dot to various locations with respect to the other. We give a detailed description of singlet-triplet dynamics near these spin-valley resonances and compare the results of calculations with measurements on double quantum dots in two distinct Si/SiGe heterostructures. Comparison of theory with experiments in which the presence of a few valley occupation patterns is visible, gives insight into the valley dependence of $g$-factors in these structures, providing support for a recently proposed theoretical model of this dependence. We also discuss how dephasing of singlet return probability oscillations near the spin-valley resonances is affected by valley splitting fluctuations caused by electric field noise.