Spin Projection and Correlation Experiments in Nanoelectronic Devices

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 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.\ In this thesis, we investigate all the above criteria using electron spin transport through engineered QDs in InAs NWs, chosen predominantly due to their large g-factors in QDs. We first show a new approach to control electron spin currents in QDs using stray magnetic fields locally generated from individual nanomagnets. Using this approach, we demonstrate electrically tunable highly efficient spin injection and detection in a double quantum dot spin valve (DQD-SV). We then use this efficient spin detection technique in a Cooper pair splitter device to perform spin readout and filtering of the CPS conductance signal. In addition, electron spin state engineering at very large magnetic fields through the Pauli spin blockade (PSB) effect is also presented

A Double Quantum Dot Spin Valve

A most fundamental and longstanding goal in spintronics is to electrically tune highly efficient spin injectors and detectors, preferably compatible with nanoscale electronics. Here, we demonstrate all these points using semiconductor quantum dots (QDs), individually spin-polarized by ferromagnetic split-gates (FSGs). As a proof of principle, we fabricated a double QD spin valve consisting of two weakly coupled semiconducting QDs in an InAs nanowire (NW), each with independent FSGs that can be magnetized in parallel or anti-parallel. In tunneling magnetoresistance (TMR) experiments at zero external magnetic field, we find a strongly reduced spin valve conductance for the two anti-parallel configurations, with a single QD polarization of $\sim 27\%$. The TMR can be significantly improved by a small external field and optimized gate voltages, which results in a continuously electrically tunable TMR between $+80\%$ and $-90\%$. A simple model quantitatively reproduces all our findings, suggesting a gate tunable QD polarization of $\pm 80\%$. Such versatile spin-polarized QDs are suitable for various applications, for example in spin projection and correlation experiments in a large variety of nanoelectronics experiments

Spin cross-correlation experiments in an electron entangler

Correlations are fundamental in describing many-body systems. However, in experiments, correlations are notoriously difficult to assess on a microscopic scale, especially for electron spins. Even though it is firmly established theoretically that the electrons in a Cooper pair(1) of a superconductor form maximally spin-entangled singlet states with opposite spin projections(2-4), no spin correlation experiments have been demonstrated so far. Here we report the direct measurement of the spin cross-correlations between the currents of a Cooper pair splitter(5-13), an electronic device that emits electrons originating from Cooper pairs. We use ferromagnetic split-gates(14,15), compatible with nearby superconducting structures, to individually spin polarize the transmissions of the quantum dots in the two electronic paths, which act as tunable spin filters. The signals are detected in standard transport and in highly sensitive transconductance experiments. We find that the spin cross-correlation is negative, consistent with spin singlet emission, and deviates from the ideal value mostly due to the overlap of the Zeeman split quantum dot states. Our results demonstrate a new route to perform spin correlation experiments in nano-electronic devices, especially suitable for those relying on magnetic field sensitive superconducting elements, like triplet or topologically non-trivial superconductors(16-18), or to perform Bell tests with massive particles(19,20)