# Spin Projection and Correlation Experiments in Nanoelectronic Devices

Bordoloi, Arunav. Spin Projection and Correlation Experiments in Nanoelectronic Devices. 2021, Doctoral Thesis, University of Basel, Faculty of Science.

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Official URL: https://edoc.unibas.ch/84831/

A key element in quantum computing applications is the ability to measure non-local correlations, known as entanglement, as well as reliably generate them. A naturally occurring source of entangled spin pairs is the superconducting condensate, from which spin singlet Cooper pairs can be split into two QDs on each side of a s-wave superconductor. Such Cooper pair splitter (CPS) devices have already been demonstrated in various systems, such as InAs nanowires (NWs), carbon nanotubes (CNTS) and graphene. A strong charge current correlation between the two output terminals has been demonstrated already, but a spin correlation, as expected for split singlet states, is missing and is even conceptually problematic so far. Such spin correlation measurements, i.e. the expectation value of the product of spin projection operators $\left<\sigma_{1} \otimes \sigma_{2}\right>$ of the two QDs in a CPS device, requires efficient spin readout of the split electrons without destroying the superconducting state of the emitter. The idea is to use the two QDs for spin filtering, achievable by applying locally different magnetic fields. A lower CPS current is then expected for the parallel spin projection axes with respect to the antiparallel ones. In general, the most essential requirements for such an complex experiment can be summarized as: (1) highly polarized QDs with large electrical tunability of the QD spin polarization for efficient spin detection in close proximity to a superconductor; (2) coexistence of superconductivity and locally varying magnetic fields in close proximity to each other, such that the critical field of the superconductor is much higher than the local magnetic field strength; and (3) the CPS current in both QDs should exhibit non-local spin correlations in a specific pattern, i.e. higher for antiparallel spin projection axes.\