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Semiconductors in the proximity of superconductors have been proposed tosupport phases hosting Majorana bound states. When the systems undergo atopological phase transition towards the Majorana phase, the spectral gapcloses, then reopens, and the quasiparticle band spin polarization is inverted.We focus on two paradigmatic semiconductor-superconductor heterostructures andpropose an all-electrical spectroscopic probe sensitive to the spin inversionat the topological transition. Our proposal relies on the indirect coupling ofa time-dependent electric field to the electronic spin due to the strong Rashbaspin-orbit coupling in the semiconductor. We analyze within linear responsetheory the dynamical correlation functions and demonstrate that some componentsof the susceptibility can be used to detect the nontrivial topological phases.

All-electrical spectroscopy of topological phases in semiconductor-superconductor heterostructures