Tight-binding simulation of Andreev spin qubits in germanium

We numerically study Andreev bound states realized in germanium with proximitized superconductivity. Starting from a Luttinger-Kohn Hamiltonian, we use a tight-binding model to show that Andreev states of opposite spin are nondegenerate at finite phase difference between superconducting leads for realistic system parameters, consistent with previous analytical results. Upon changing the aspect ratio of the geometry, we can optimize the effective qubit frequency. Moreover, we characterize the spin and heavy- and light hole weight of the Andreev states as a function of phase difference which allows us to predict the expected magnetic- and electric-noise induced decoherence rates. Lastly, upon departing from singlet superconductiviy, we find that, when the heavy hole-light hole splitting is large compared to the superconducting gap, the Andreev frequencies are largerly independent of the superconductivity induced in the light-hole sector.