Search for genons in fractional Chern insulator states on an infinite cylinder

For topological phases of matter on a lattice, the presence of lattice defects can have dramatic effects. A remarkable example is represented by genons [1], quasiparticles bound to lattice dislocations and associated to an effective increase in the genus of the underlying surface. We consider the Hofstadter butterfly spectrum generated by a periodic potential with square symmetry and identify several subbands that have the potential to host genons. We perform infinite cylinder DMRG simulations [2] of interacting electrons at appropriate filling of these subbands and find fractional Chern insulator (FCI) ground states. The topological degeneracy of these states is expected to depend on the number m of unit cells that fit in the cylinder circumference, namely on its parity (as even and odd values are related by creating a pair of dislocations and dragging them to infinity). We thus search for evidence of the presence of genons by performing numerical flux threading experiments aimed at measuring the topological degeneracy of the FCI ground states.

[1] M. Barkeshli and X.-L. Qi, PRX 2, 031013 (2012)
[2] M. P. Zaletel et al., PRB 91, 045115 (2015)