Gate tunable spin splitting of germanium quantum well Josephson junction

Proximitized Ge heterostructures are a promising host platform for Andreev qubits and topological qubits because of their strong spin-orbit coupling, high mobility, and naturally low abundance of nuclear spins [1]. An important distinction between Ge and traditional Andreev qubit materials like InAs is the form of their Rashba spin-orbit coupling, which is linear in momentum for InAs but cubic for Ge. Here, we compare the effects of linear vs cubic spin-orbit coupling on the spin splitting of the Andreev bound spectrum. Our numerical calculations indicate a different power-law dependence of the spin splitting on the spin-orbit coefficient for these two cases. Moreover, these two cases show distinct spin-splitting behavior as a function of chemical potential and junction width. These results point towards optimal geometries and device tunings for implementing Andreev qubits in future experiments.