Exploring the effect of spin configurations in a three-site Kitaev chain

Kitaev chains in superconductor-semiconductor hybrids have emerged as a viable platform for engineering Majorana Bound States (MBSs). These chains have now been implemented with two and three sites. However, scaling to longer chains is desirable since the protection of the MBSs scales exponentially with the number of sites. When a Kitaev chain is extended to N sites, flux control over all superconducting phases is required, which would naively require N-1 superconducting loops and N-1 flux bias lines. Here, we study a three-site Kitaev chain, and show that the relative phase between the interdot couplings is dependent on the specific spin configuration. Therefore, by controlling the spin on each quantum dot, purely through electrostatics, we effectively eliminate the need for external flux control. This idea was recently proposed theoretically [1], and significantly relaxes the requirements for the practical implementation of longer Kitaev chains.



[1] Chun-Xiao Liu et al. ‘Protocol for scaling up a sign-ordered Kitaev chain without magnetic flux control’, Arxiv (2024).