Critical Lengths of Kitaev Chains for Majorana Zero Modes with a Microsecond Coherence Time and a Quantized...

The problems of disorder and insufficient system length are generally regarded as central problems in the realization of Majorana zero modes (MZM), which are a promising platform for realizing fault-tolerant topological quantum computing (TQC). In this work, we analyze eigenenergy spectra and transport properties of finite Kitaev chains using quantum transport simulations in a wide design space of hopping amplitude (t), superconductor pairing (Δ), and electrochemical potential. Our goal is to determine critical or minimum acceptable chain lengths to obtain oscillation-free MZMs with suitable microsecond coherence times, and observable zero-bias conductance peaks (ZBCP) quantized almost at ~2e²/h. Due to qualitative equivalence of the Kitaev and Oreg-Lutchyn models, we approximately determine the foreseeable critical length of topological superconducting nanowires (TS NWs) as well. We find that the ZBCP length requirement is looser in comparison to the limit imposed by the coherence time. For a large t/Δ mismatch of ~40 corresponding to the experimental TS NWs, the first condition sets the minimum length to 344 sites (≈5.5 μm), while the second condition requires 605 sites (≈9.7 μm). The calculated lengths are far from the reported experimental hybrid device dimensions, explaining difficulties in observing MZMs in TS NWs fabricated so far. Nonetheless, a decreasing t/Δ mismatch allows for shorter systems, which argues in favor of the proximitized quantum dot path for MZMs in a solid-state system.