Laboratoire de Physique Théorique
Toulouse - UMR 5152

The many-body physics of interacting particles in topological flat bands mirrors the rich physics of the fractional quantum Hall effect. Such bands may arise from artificial magnetic fields and can be achieved in optical lattice configurations of cold atoms or potentially in 2D materials with strong spin-orbit coupling. These systems support quantum liquids within the same universality class as continuum fractional quantum Hall states in the case of bands with Chern number one [1]. However, lattice models also allow for bands with higher Chern numbers, giving rise to novel states, including the composite fermion series with band filling factors $\nu = r/(r|C| +1)$ for bosons, or $\nu = r/(2r|C| +1)$ for fermions, where $r$ is an integer [3,4].

FQH liquids in higher Chern bands are also predicted to support "genons", a new class of non-Abelian defects associated with dislocations [5]. So far, there has been no convincing numerical demonstration of this effect, due to the enhanced complexity of simulating models without translational symmetry. Here, I will report a detailed numerical study of these extrinsic wormhole-like defects, based on a lattice model with a local Hamiltonian constructed by exploiting the relation of higher Chern bands to multi-layer fractional quantum Hall systems. I will provide direct evidence for the non-Abelian statistics of the defects by counting the associated quasiparticle degeneracies [6]. Our results indicate that genons can be created in the laboratory by combining the physics of artificial gauge fields in cold atom systems with already existing holographic beam shaping methods for creating wormhole-like defects.

[1] T. Scaffidi, & G. Möller Phys. Rev. Lett. 109, 246805 (2012).

[2] T. Jackson, G. Möller, R. Roy, Nature Communications 6, 8629 (2015).

[3] G. Möller, N.R. Cooper, Phys. Rev. Lett. 103, 105303 (2009).

[4] G. Möller, N.R. Cooper, Phys. Rev. Lett. 115, 126401 (2015).

[5] M. Barkeshli & X.-L. Qi, Phys. Rev. X 2, 031013 (2012).

[6] Z. Liu, G. Möller, E. Bergholtz, arxiv:1702.05115.