Second Order Topological Superconductivity: Majorana and parafermion corner states

Jelena Klinovaja


Recently, a lot of interest has been raised by the generalization of conventional TIs/TSCs to so-called higher order TIs/TSCs. While a conventional d-dimensional TI/TSC exhibits (d − 1)-dimensional gapless boundary modes, a d-dimensional n-th order TI/TSC hosts gapless modes at its (d − n)-dimensional boundaries. In my talk, I will consider a Josephson junction bilayer consisting of two tunnel-coupled two-dimensional electron gas layers with Rashba spin-orbit interaction, proximitized by a top and bottom s-wave superconductor with phase difference φ close to π [1-3]. In the presence of a finite weak in-plane Zeeman field, the bilayer can be driven into a second order topological superconducting phase, hosting two Majorana corner states (MCSs). If φ=π, in a rectangular geometry, these zero-energy bound states are located at two opposite corners determined by the direction of the Zeeman field. If the phase difference φ deviates from π by a critical value, one of the two MCSs gets relocated to an adjacent corner. As the phase difference φ increases further, the system becomes trivially gapped. The obtained MCSs are robust against static and magnetic disorder.

In the second part of my talk, I will switch from non-interacting systems [4,5], in which one neglects effects of strong electron-electron interactions, to interacting systems and, thus, to exotic fractional phases. I will show that this is indeed possible and explicitly construct a two-dimensional (2D) fractional second-order TSC. I will consider a system of weakly coupled Rashba nanowires in the strong spin-orbit interaction (SOI) regime. The nanowires are arranged into two tunnel-coupled layers proximitized by a top and bottom superconductor such that the superconducting phase difference between them is π. In such a system, strong electron- electron interactions can stabilize a helical topological superconducting phase hosting Kramers partners of Z_2m parafermion edge modes, where m is an odd integer determined by the position of the chemical potential. Furthermore, upon turning on a weak in-plane magnetic field, the system is driven into a second- order topological superconducting phase hosting zero-energy Z_2m parafermion bound states localized at two opposite corners of a rectangular sample.


[1] Y. Volpez, D. Loss, and J. Klinovaja, Phys. Rev. Lett. 122,126402 (2019)

[2] K. Plekhanov, M. Thakurathi, D. Loss, and J. Klinovaja, Phys. Rev. Research 1, 032013(R) (2019)

[3] K. Plekhanov, N. Müller, Y. Volpez, D. M. Kennes, H. Schoeller, D. Loss, and J. Klinovaja, arXiv:2008.03611

[4] K. Laubscher, D. Loss, and J. Klinovaja, Phys. Rev. Research 1, 032017(R) (2019)
[5] K. Laubscher, D. Loss, and J. Klinovaja, Phys. Rev. Research 2, 013330 (2020)