From Majorana to parafermion corner states in second-order topological superconductors

Recently, the generalization of conventional topological insulators (TIs) and topological superconductors (TSCs) to so-called higher-order TIs and TSCs has raised significant interest. While conventional d-dimensional TIs and TSCs host gapless edge states at their (d-1)-dimensional boundaries, nth-order d-dimensional TIs and TSCs exhibit gapless edge states at their (d-n)-dimensional boundaries. In particular, a two-dimensional second-order TSC (SOTSC) hosts Majorana bound states at the corners of a rectangular sample. Here, we demonstrate how the presence of strong electron-electron interactions can ‘fractionalize’ such Majorana corner states [1,2] and promote them to even more exotic parafermion corner states. [3,4] For this, we construct an SOTSC from an array of weakly coupled one-dimensional wires, which allows us to treat the strong interactions analytically using bosonization techniques. As a possible platform to realize such a system, we discuss coupled helical channels in gated bilayer graphene.

 

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

[2] K. Laubscher and J. Klinovaja, Journal of Applied Physics 130, 081101 (2021).

[3] K. Laubscher, D. Loss, and J. Klinovaja, Phys. Rev. Research 1, 032017(R) (2019).

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