Direct Measurement of the Andreev Bound State Spin and Charge During the Singlet-Doublet Transition*

The past decade has seen many proposals to measure Majorana quasi-particles definitively. One such measurement involves probing the bulk spin polarization of a system undergoing a topological phase transition. An Andreev bound state (ABS) is expected to similarly show both charge and spin reversal at the singlet-doublet quantum phase transition. 

In this talk, we demonstrate a direct measurement of the spin and charge of an ABS. We measure the spin of the ABS by coupling it to a spin-polarized quantum dot and track its evolution as a function of magnetic field and chemical potential. We also measure the charge of the ABS by using non-local spectroscopy. Considering the ABS as a model for a topological system, we observe the expected signal at the quantum phase transition. We propose to extend these techniques as complementary measures for the occurrence of a topological phase transition.