Vortex bound states of charge and magnetic fluctuations induced topological superconductors in heterostructures

The helical electron states on the surface of topological insulators or elemental bismuth become unstable toward superconducting pairing formation when coupled to the charge or magnetic fluctuations. The latter gives rise to pairing instability in chiral channels $d_{xy}\pm i{d}_{x^2-y^2}$, as has been observed recently in the epitaxial Bi/Ni bilayer system at relatively high temperature, while the former favors a pairing with zero total angular momentum. Motivated by this observation we study the vortex bound states in these superconducting states. We consider a minimal model describing the superconductivity in the presence of a vortex in the superconducting order parameter. We show that zero-energy states appear in the spectrum of the vortex core for all pairing symmetries. Our findings may facilitate the observation of Majorana modes bounded to the vortices in heterostructures with no need for a proximity-induced superconductivity and relatively large value of $\mathrm{\Delta }/E_F$.

Figure 1

A schematic representation of epitaxial bilayer. A thin film of bismuth (Bi) or topological insulator (TI) is deposited on a ferromagnetic layer such as nickel (Ni), an experimentally realized bilayer [26]. The Dirac cone and the black arrows indicate the helical electron states near the Fermi surface. The wavy red line shows the pairing states between electron states living on opposite sides of the Fermi surface, induced by the magnetic fluctuations on the in-plane magnetic moments (thick blue arrow) of nickel. Vertical arrows demonstrate a schematic view of a typical vortex.