Excess Vortex-Vortex Supercurrent as Method for Readout of Majorana Parity in Fe(Se,Te)

Topological superconductors are one of the most exciting new platforms for the development of topological quantum computing. Specifically, the Fe(Se,Te) family has been shown to host Majorana zero-energy modes (MZMs) in vortex cores [1], pairs of which can potentially be used as topologically protected qubits. However, there has been no previous calculations to suggest that the two distinct parity states can be distinguished experimentally. Through the use of an effective two-dimensional Fu-Kane model on the surface of FeTe_xSe_1-x, we approximate the (p_x + ip_y) superconductor as an internal s-wave proximity effect on the topological surface states. We then numerically calculate the wavefunction solution to the resulting Bogoliubov-de Gennes equation for both spatially separated single vortices and the double vortex limit of complete overlap of the single vortex pair. Using these wavefunction solutions, we compute supercurrent generated by zero-energy mode splitting and the resulting magnetic field gradient above the surface. We conclude it is possible to measure the presence of this excess supercurrent, and thus the quantum state of the MZM pair, using magnetic force microscopy.
[1] T. Machida, Nature Materials 18, 811–815 (2019).