Unconventional Superconductivity on a Topological Insulator

We study proximity-induced superconductivity on the surface of a topological insulator (TI), focusing on unconventional pairing. We find that the excitation spectrum becomes gapless for any spin-triplet pairing, such that both subgap bound states and Andreev reflection is strongly suppressed. For spin-singlet pairing, the zero-energy surface state in the $d_{xy}$-wave case becomes a Majorana fermion, in contrast with the situation realized in the topologically trivial high-$T_c$ cuprates. We also study the influence of a Zeeman field on the surface states. Both the magnitude and direction of this field are shown to strongly influence the transport properties, in contrast with the case without TI. We predict an experimental signature of the Majorana states via conductance spectroscopy.

Figure 1

We consider a TI where superconductivity and/or magnetic correlations are induced on the surface via the proximity effect to host materials with the desired properties.

Figure 2

Plot of the dispersion for the bound-state energies for several values of the Zeeman field $m_z$. As $m_z\to 0$, one obtains $|\epsilon |\to \Delta$ in the $s$-wave case and $|\epsilon |\to 0$ in the $d_{xy}$-wave case. We have set ${\mu }_{\mathrm{S}}/{\Delta }_0=100\gg {\mu }_{\mathrm{N}}/{\Delta }_0$. The energy dispersion changes sign when $m_z$ changes sign.

Figure 3

Plot of the tunneling conductance $G/G_0$ for an $\mathrm{N}\mid \mathrm{FI}\mid \mathrm{S}$ junction in the $s$-wave and $d_{xy}$-wave case. We have set $\mu L/v_F=1$.