The Nonlocal Josephson Effectin Systems Based on KitaevChains : A study on Josephson transport mediated by hybridized Andreev bound states

Sammanfattning

On their own, superconductors exhibit a multitude of exotic quantum phenomena, especially when superconducting regions are coupled through non-superconducting barriers. In such systems, known as Josephson junctions, a supercurrent can flow even in the absence of a voltage bias. The microscopic transport mechanism is governed by repeated Andreev reflections, a cyclic process with explicit phase dependence, identified as the transport of Cooper pairs via Andreev bound states. Through parameter choices, a superconductor may reside in either a trivial or a topological regime, characterized by its low-energy spectra and, in the topological regime, the emergence of Majorana zero modes found at the system boundaries. In systems of finite length, the Majorana zero modes may hybridize, leading to a distinct separation from the zero-level, exposing the system to quantum decoherence. Inversely, a system residing in the topological regime housing non-hybridized Majorana zero modes can thus be considered topologically protected against quantum decoherence, allowing for a great range of technologies, e.g. superconducting interference devices and quantum bits. Further exotic phenomena appear with the coupling of multiple Josephson junctions, moving from an S-N-S geometry identified by a superconducting region, normal region, superconducting region to a more complex S-N-S-N-S geometry, extended by a further superconducting region, normal region. This gives rise to nonlocal effects, where the phase difference across one Josephson junction may impact the current over another Josephson junction. Implications are potential applications in quantum computation and sensing devices. This paper studies the nonlocal Josephson effect in junctions formed by Kitaev chains. The trivial phase of a Kitaev chain Josephson junction shows a gapped spectrum, while the topological phase hosts Majorana zero modes. In long chains, the junction hosts two Majorana zero modes for any phase difference φ and four at φ = π; short chains show zero-energy splitting at φ = π. TheJosephson current is enhanced in the topological phase for long chains. We then analyze a three-chain setup, representing two coupled Josephson junctions. Hybridization of topological Andreev-bound states occurs when the middle chain is short, disperses with a phase difference, and can be controlled by the phase across the right junction. This hybridization enables a highly tunable Josephson current, revealing the nonlocal Josephson effect.