Andreev Spin Qubits in Germanium-Based Josephson Junctions

We theoretically study Andreev bound states realized in a quasi-one-dimensional superconductor|germanium|superconductor heterostructure. In the absence of magnetic fields and perfect contact between the superconductor and semiconductor in the Josephson junction, we generate an analytic formula for the energy and wavefunctions of the Andreev states as a function of phase difference between the superconductors. As a result of the interaction between the effective heavy- and light-hole bands, there exists two fermi velocities in the underlying semiconductor which results in an effective spin splitting of the Andreev states in the absence of time reversal symmetry. Consequently, we identify this system as a potential candidate for the realization of Andreev spin qubits. We perturbatively study the effect of a magnetic field and imperfect contacts, using the aforementioned analytic wavefuctions, and we also construct a tight-binding simulation to account for such effects exactly.