Chirality inversion of Majorana edge modes in a Fu–Kane heterostructure

Fu and Kane have discovered that a topological insulator with induced s-wave superconductivity (gap Δ0, Fermi velocity v F, Fermi energy μ) supports chiral Majorana modes propagating on the surface along the edge with a magnetic insulator. We show that the direction of motion of the Majorana fermions can be inverted by the counterflow of supercurrent, when the Cooper pair momentum along the boundary exceeds \({{\Delta}}_{0}^{2}/\mu {v}_{\mathrm{F}}\). The chirality inversion is signaled by a doubling of the thermal conductance of a channel parallel to the supercurrent. Moreover, the inverted edge can transport a nonzero electrical current, carried by a Dirac mode that appears when the Majorana mode switches chirality. The chirality inversion is a unique signature of Majorana fermions in a spinful topological superconductor: it does not exist for spinless chiral p-wave pairing.