Analyzing Cooper pair injection and induced superconducting correlations in hybrid nanowire systems*

The ability to induce a superconducting gap in a semiconducting nanowire via the proximity effect plays a key role in many applications [1-2], including topological quantum computation.  The study of the proximity effect [3-4], therefore is a very important aspect. In this work, we provide a detailed analysis of the proximity effect using the Keldysh non-equilibrium Green’s function (NEGF) formalism, coupling together the understanding of induced correlations with quantum transport. We first consider a ferromagnetic proximity effect in a normal-ferromagnetic hybrids and analyze the decay of the induced order parameter and characterise it against disorder. We then study the proximity effect in normal-superconducting and ferromagnetic-superconducting hybrids, and discuss the physics of the proximity within and outside of the Andreev approximation. Within this formalism, we also comment on the inverse proximity effect in the superconductor using the ferromagnetic-superconducting case as an example. Using these theoretical tools, we analyse recent experimental proposals of enhanced Cooper pair injection via creation of resonant levels. Lastly, we extend our analysis to two dimensions by considering more exotic induced effects by analysing a superconductor-quantum-Hall-insulator hybrid junction.

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[1] Nat. comms. 10.1 (2019): 5128.

[2] Comms. Physics 6.1 (2023): 36.

[3] Phys. Rev. B 65.1 (2001): 014509.

[4] Phys. Rev. B 102.13 (2020): 134211