Higher order effective coefficients in Ge/Si core/shell nanowire devices

Germanium based nanowires are prominent platforms in mesoscopic physics because of their tunable spin-orbit interaction. This property makes them an interesting candidate for hole-qubit devices or as a platform for Majoranas. Hence, a good understanding of effective models for the relevant degrees of freedom in these devices is of great importance. We revisit the subject of effective Hamiltonians and effective coefficients for efficient nano-device control in Ge/Si core/shell semiconductor nanowires from a perturbation theory perspective. We elaborate on relevant terms and present numerical and semi-analytical results of Löwdin perturbation theory to second order. We discuss the consequences of higher order terms on the effective models of interest for device applications.