Understanding Gate Modulation of G-factor in Germanium Spin Qubits

The g-tensor is a key parameter in the control of spin qubits, as it directly influences a qubit’s response to external magnetic fields. Recent experiments by Rooney et al. demonstrated that the g-tensor can vary by an order of magnitude with slight adjustments in gate voltage, likely due to strain induced by thermal contraction [1]. However, a quantitative description of this effect remains lacking, and this study aims to fill that gap. When cooled to cryogenic temperatures, the differing thermal contraction rates between the gates and substrates create an inhomogeneous strain profile, leading to corrections to the unstrained g-tensor [2]. In this work, we first calculate the strain distribution by solving the thermoelasticity equation using the Finite Element Method (FEM) with FEniCS. Next, we solve Schrödinger’s equation with an electric potential background obtained from Poisson’s equation using a high-order finite difference method to model the electron density distribution as a function of gate voltage. Finally, we compute the strain-induced g-tensor corrections for the quantum dot under varying voltages, finding that the in-plane effective g-factor can change by up to a factor of 2. This talk will summarize our methods and results, and explore the implications for Singlet-Triplet and Zeeman qubit control.

[1] Rooney, John, Zhentao Luo, Lucas E. A. Stehouwer, Giordano Scappucci, Menno Veldhorst, and Hong-Wen Jiang. “Gate Modulation of the Hole Singlet-Triplet Qubit Frequency in Germanium.” arXiv, November 16, 2023. http://arxiv.org/abs/2311.10188.

[2] Abadillo-Uriel, José Carlos, Esteban A. Rodríguez-Mena, Biel Martinez, and Yann-Michel Niquet. “Hole-Spin Driving by Strain-Induced Spin-Orbit Interactions.” Physical Review Letters 131, no. 9 (September 1, 2023): 097002. https://doi.org/10.1103/PhysRevLett.131.097002.