Material challenges and opportunities for Ge/GeSi heterostructures: a modelling perspective

Hole spin qubits in strained Ge/GeSi heterostructures have made outstanding progress in the past five years, with demonstrations of more than ten qubit devices. Yet Ge/GeSi heterostructures face specific challenges for scaling, such as plastic strain relaxation and a strong g-factor anisotropy that hinders the optimization of the magnetic field orientation. The figures of merit (Rabi frequencies, lifetimes...) can indeed vary by an order of magnitude within a few degrees around the heterostructure plane. Here we discuss material challenges and opportunities for Ge/GeSi heterostructures from a modelling perspective. We address, in particular, the prospects for bulk Germanium devices, where the holes are confined at the interface between an unstrained Ge substrate and an epitaxial GeSi barrier. Owing to the absence of strains, the heavy-hole/light-hole mixing is much stronger in such heterostructures, which reduces the gyromagnetic anisotropy and enhances spin-orbit coupling. This increases the Rabi frequency f_R and quality factor Q = f_RT₂^* of the qubits despite a small reduction of the coherence time T₂^*. We compare the strengths and weaknesses of strained and unstrained heterostructures and draw the perspectives for, e.g., spin-photon coupling.