Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator

We study the proximity effect between an $s$-wave superconductor and the surface states of a strong topological insulator. The resulting two-dimensional state resembles a spinless $p_x+i{p}_y$ superconductor, but does not break time reversal symmetry. This state supports Majorana bound states at vortices. We show that linear junctions between superconductors mediated by the topological insulator form a nonchiral one-dimensional wire for Majorana fermions, and that circuits formed from these junctions provide a method for creating, manipulating, and fusing Majorana bound states.

Figure 1

(a) A STIS line junction. (b) Spectrum of a line junction for $W=\mu =0$ as a function of momentum for various $\varphi$. The solid line shows the Andreev bound states for $\varphi =\pi$. The dashed lines are for $\varphi =3\pi /4$, $\pi /2$, and $\pi /4$. The bound states for $\varphi =0$ merge with the continuum, indicated by the shaded region. (c) A trijunction between three superconductors. (d) Phase diagram for the trijunction. In the shaded regions there is a $\pm$ MBS at the junction.

Figure 2

Energy levels in units of $\Delta E=\tilde{v}/L$ for a STIS line junction terminated by two trijunctions as a function of $\delta ={\Delta }_0\cos \varphi /2$ for $\varphi \sim \pi$. In (a) two MBSs are created or fused when $\varphi$ passes through $\pi$. In (b) a single MBS is transported from one end to the other. The insets depict the MBSs.

Figure 3

Simple circuits made from STIS junctions. When $\varphi$ is advanced from 0 to $2\pi$, (a) produces an entangled state and (b) interchanges MBSs 1 and 2.