Abstract: In this talk I will first review the properties of toy-models for topological superconductivity, the Kitaev chain and its generalizations. After discussing the topological phase diagram of the isolated system, using a scattering technique within the Bogoliubov–de Gennes formulation, I will discuss the differential conductance properties as a function of all relevant model parameters. The relevant problem of implementing local spectroscopic measurements to characterize the Majorana fermions useful in quantum technologies is also addressed. We will also show how topological protection can be lost when the quantum states of an initially isolated topological system are hybridized with those of the external reservoirs. Finally, I will present a novel platform for topological superconductivity based on 2DEGs at LAO/STO interface. Here the interplay of spin-orbit interaction and intrinsic superconductivity may induce a topological phase transition in an applied magnetic field with strong orbital character[2,3]. The conclusions will address the design of various nanowire-based mesoscopic devices for topological computation[4,5].
 A. Maiellaro; F. Romeo; C.A. Perroni, V. Cataudella; R. Citro, Unveiling Signatures of Topological Phases in Open Kitaev Chains and Ladders, Nanomaterials 9, 894 (2019)
 C.A. Perroni, V. Cataudella, M. Salluzzo, M. Cuoco and R. Citro, Evolution of topological superconductivity by orbital selective confinement in oxide nanowires, Physical Review B, 100, 094526 (2019)
 J. Settino, F. Forte, C. A. Perroni, V. Cataudella, M. Cuoco, and R. Citro, Spin-orbital polarization of Majorana edge states in nanowire oxides, Physical Review B 102, 224508 (2020)
 A. Barthelemy, N. Bergeal, M. Bibes, A. Caviglia, R. Citro, M. Cuoco, A. Kalaboukhov, B. Kalisky, C. A. Perroni,J. Santamaria, D. Stornaiuolo and M. Salluzzo, Quasi-two-dimensional electron gas at the oxide interfaces for topological quantum physics, Eur. Phys. Lett., 133, 17001 (2021)
 G. Singh et al. Gate-tunable pairing channels in superconducting non-centrosymmetric oxides nanowires, npj Quantum Materials 7, 2 (2022)
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