# CAMP: Transport in Topological Insulators and Topological Superconductors: In Search of Majorana Fermions

## Main Content

Topological insulators (TIs) have a bulk energy gap that separates the highest occupied band from the lowest unoccupied band while gapless energy electronic states that are protected by time reversal symmetry live at the edge (2D TIs) or surface (3D TIs) [1]. Similarly, topological superconductors have gapless zero energy states protected by the particle-hole symmetry, which in some cases form Majorana bound states. In this talk, we focus on the proximity-induced superconductivity in TIs as well as on unusual properties of topological superconductors showing that they both can pave a road to find a Majorana state.

S-wave superconductor on the top of the surface states of 2D or 3D TI generates mixed order parameter (s-wave and p-wave pairing mixture in the surface state), due to the spin-momentum locking. The central theoretical task is to obtain information about this unconventional p-wave component. We find that in the Josephson junction setup, namely superconductor (S) /surface state of topological insulator/superconductor (S), existence of these two superconducting channels leads to novel features in transport [2]. In particular, the topological Andreev bound state (ABS) (the state of hybridized two helical Majorana fermions)) occurs for the normal incidence where ABS is protected against backscattering [2]. This topological helical ABS is characterized by the novel effect, which we dubbed superconducting Klein tunnelling (tunnelling of the helical ABS with the transmission one through the normal regime independent of the barrier strength). Further, we propose the experimental setups to observe the topological helical ABS in 2D and 3D TIs hybrid structures [3,4].

Finally, we discuss new systems like topological superconductors on the hexagonal lattices as well as theoretical schemes that could allow to measure edge conductance in these materials [5]. Is there a way to measure Majorana state in these systems?

[1] G. Tkachov and E. M. Hankiewicz, topical review in *Phys. Status Solidi B* **250**, 215 (2013).

[2] G. Tkachov and E. M. Hankiewicz, *Phys. Rev. B* **88**, 075401 (2013).

[3] I. Sochnikov, L. Maier, C. A. Watson, J. R. Kirtley, C. Gould, G. Tkachov, E. M. Hankiewicz, C. Brüne, H. Buhmann, L. W. Molenkamp, and K. A. Moler, *Phys. Rev. Lett.* **114**, 066801 (2015).

###### [4] G. Tkachov, P. Burset, B. Trauzettel, and E. M. Hankiewicz *Phys. Rev. B* **92**, 045408 (2015).

[5] L. Elster, C. Platt, R. Thomale, W. Hanke, and E. M. Hankiewicz, arXiv:1408.3551, accepted to *Nat. Comm. *(2015).