Detection of Majorana zero modes bound to Josephson vortices in planar superconductor--three-dimensional topological insulator--superconductor junctions

We study signatures of Majorana zero modes (MZMs) bound to Josephson vortices in superconductor--three-dimensional topological insulator--superconductor (S--TI--S) Josephson junctions placed in a perpendicular magnetic field. First, using semiclassical analytical as well as numerical techniques, we calculate the spatially resolved supercurrent density carried by the low-energy Caroli-de Gennes-Matricon (CdGM) states in the junction and discuss if and how the presence of vortex MZMs is reflected in supercurrent measurements. We show that Fraunhofer signatures alone are not suitable to reliably detect vortex MZMs, such that supercurrent measurements should always be complemented with additional measurements to further verify that the junction does indeed host MZMs. We discuss how such additional Majorana signatures could be obtained by (1) mapping out the local density of states in the junction via scanning tunneling microscopy techniques, and (2) microwave spectroscopy of the spectrum of low-energy CdGM states in the junction.