Systems of strongly interacting particles, fermions or bosons, can give rise to topological phases that are not accessible to non-interacting systems. For instance all non-interacting phases of bosons are topologically trivial but interactions can bring about various non-trivial phases such as the bosonic fractional quantum Hall states. Many interaction-enabled topological phases have been discussed theoretically but, aside from the well known fractional quantum Hall states, few experimental realizations exists.

This project focuses on theoretical analyses of natural or artificially engineered structures in which interactions between particles dominate over their kinetic energy and can at the same time give rise to topologically non-trivial phases. One such structure consists of a topological insulator interfaced with an ordinary superconductor (see Figure 1). According to Fu and Kane [1] vortices in such an interface host Majorana zero modes. Furthermore, in the presence of a vortex lattice there exists a regime in which hopping between the adjacent Majorana fermions is strongly suppressed, the so called "neutrality point" [2]. Close to the neutrality point the kinetic energy of the Majorana fermions is quenched and the low-energy physics is controlled by fermion interactions. Depending on the details of the vortex lattice geometry various interesting one- and two-dimensional models can arise. In some cases they form interaction-enabled topological phases (see Figure 2 for an example) that fundamentally cannot exist in weakly interacting systems [3,4].

More generally, this collaboration is aimed at exploring the interplay between strong interactions and topology in systems that can be potentially realized in a laboratory. These include

- Magnetic and superconducting phases in surfaces of three-dimensional topological insulators

- Interaction effects in systems with flat bands that exhibit non-trivial topology

- Emergence and stability of Majorana fermions in heterostructures involving topological

insulators in reduced dimensions (wires, 2D films)

- Realistic physical systems that can host exotic particles such as parafermions and

Fibonacci anyons

**References**

[1] L. Fu and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008).

[2] C.-K. Chiu, D.I. Pikulin, and M. Franz, Phys. Rev. B. 91, 165402 (2015).

[3] M.F. Lapa, J.C.Y. Teo and T.L. Hughes, Phys. Rev. B 93, 115131 (2016).

[4] C.-K. Chiu, D.I. Pikulin, and M. Franz, Phys. Rev. B 92, 241115 (2015).

[5] A. Rahmani, Xiaoyu Zhu, M. Franz, and I. Affleck, Phys. Rev. Lett. 115, 166401 (2015).

**Principal Investigators**

M. Franz (UBC) franz@physics.ubc.ca

J.H. Bardarson (MPI-PKS) jensba@pks.mpg.de

D. Manske (MPI-FKF) d.manske@fkf.mpg.de

Ian Affleck (UBC)

A. Schnyder (MPI-FKF)