Majorana fusion rules in a single-charge topological transistor*

By now, there has been a lot of evidence of the existence of Majorana fermions at the ends of topological superconductors, hosting Majorana bound states (MBSs) at theis ends [1]. A demonstration of the theoretically predicted non-abelian properties of MBSs would constitute a definite proof of a topological superconducting phase, paving the way towards future topological quantum computing. Alongside the nontrivial braiding statistics, the fusion rules are fundamental properties of all non-abelian anyons. 

 

We propose a way to demonstrate MBS fusion rules in a topological single-charge transistor. Our proposal reduces both the number of operations and the device complexity compared with previous proposals [2]. Furthermore, we show that the fusion protocol can be adapted to pump a quantized and topologically protected amount of charge in each cycle, opening up for detecting fusion through DC current measurements. We analyze the protocol numerically and analytically and show that the required operational timescales and expected measurement signals are within experimental capabilities in various superconductor-semiconductor hybrid platforms [3].

 

[1] R. Lutchyn et al. Nat. Rev. Mat. 3, 52 (2019).

[2] D. Aasen, Phys. Rev. X 6, 031016 (2016).

[3] R. Seoane Souto and M. Leijnse. To appear soon