Topological Superconductivity with and without time-reversal symmetry.

In the first part of my talk I will discuss the realization of a time-reversal invariant topological superconductor (TRITOPS) in one dimension. This phase is characterized by having a bulk gap, while supporting a Kramers’ pair of zero-energy Majorana bound states at each of its ends. We establish that this phase cannot be realized in a non-interacting system coupled to a conventional s-wave superconductor. We present and study a general simple model which is driven into the TRITOPS phase by repulsive interactions, and propose two proximity-coupled systems which are described by this model at low-energies. The effect of interactions is studied analytically using both a mean-field approach and the renormalization group. We corroborate our conclusions numerically using DMRG.

In the second part I will discuss signatures of Majorana bound states (MBSs) in current correlations. We study a T-junction composed of a grounded topological superconductor and of two normal-metal leads which are biased at a voltage V. We show that the existence of the MBS dictates a universal behavior for the cross correlation of the currents through the two normal-metal leads of the junction. The cross correlation is negative and approaches zero at high bias voltages as -1/V. This behavior is robust in the presence of disorder and multiple transverse channels, and persists at finite temperatures. We discuss how this behavior is related to the non-local nature of MBSs. An accidental low-energy Andreev bound state, on the other hand, gives rise to non-universal behavior of the cross correlation.

[1] A Haim, E Berg, K Flensberg, Y Oreg, arXiv:1605.07179

[2] A Haim, K Wölms, E Berg, K Flensberg, Y Oreg, arXiv:1605.09385

[3] A Haim, A Keselman, E Berg, Y Oreg, Phys. Rev. B, 89, 220504(R) (2014)

[4] A Haim, E Berg, F von Oppen, Y Oreg, Phys. Rev. B, 92, 245112 (2015)

[5] A Haim, E Berg, F von Oppen, Y Oreg, Phys. Rev. Lett. 114, 166406 (2015)