Assessing Majorana quality in few-site Kitaev chains coupled to a quantum dot

In the last two years, the engineering of Kitaev chains made from quantum dots coupled by superconductors has marked a major breakthrough towards topological quantum computing. These devices can host Majorana bound states (MBS) upon precise tuning of their parameters. However, the quality of MBS in short chains remains an open question, critical for the performance of future qubits. Here, we test the Majorana localization in two- and three-site Kitaev chains using the Prada-Clarke test [1,2]. Our device can be configured as either a two-site or a three-site Kitaev chain, coupled to an additional quantum dot. By sweeping the energy level of the quantum dot, we probe the energy splitting of the MBS at the edges of the Kitaev chain. This splitting arises from a partial overlap of the MBS wavefunctions, resulting for instance in a finite Majorana polarization. Notably, this can result from either a finite Zeeman energy or imperfect device tuning—not being precisely at the sweet spot. Our experimental results reveal that the three-site Kitaev chain exhibits superior Majorana localization compared to the two-site chain. Specifically, the three-site configuration shows reduced energy splitting during the Prada-Clarke dot energy sweep, indicating better isolation of the MBS. These findings underscore the crucial role of chain length and precise device tuning in Majorana quality, providing valuable insights into MBS behavior in short Kitaev chains.



[1] Elsa Prada, Ramón Aguado, and Pablo San-Jose, "Measuring Majorana nonlocality and spin structure with a quantum dot." Physical Review B 96.8 (2017): 085418.

[2] David J. Clarke, "Experimentally accessible topological quality factor for wires with zero energy modes." Physical Review B 96.20 (2017): 201109.