Proximity-induced Josephson π-Junctions in Topological Insulators

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We study two microscopic models of topological insulators in contact with an s-wave superconductor. In the first model the superconductor and the topological insulator are tunnel coupled via a layer of scalar and of randomly oriented spin impurities. Here, we require that spin-flip tunneling dominates over spin-conserving one. In the second model the tunnel coupling is realized by an array of single-level quantum dots with randomly oriented spins. It is shown that the tunnel region forms a π-junction where the effective order parameter changes sign. Interestingly, due to the random spin orientation the effective descriptions of both models exhibit time-reversal symmetry. We then discuss how the proposed π-junctions support topological superconductivity without magnetic fields and can be used to generate and manipulate Kramers pairs of Majorana fermions by gates.