Anyon Chern bands of opposite sign and reversed drift

Abstract

The elementary charged excitations of fractional quantum Hall states are anyons. Without continuous translation symmetry, they acquire a dispersion and richer dynamics. We study the Laughlin quasihole at filling $1/3$ in a periodically modulated magnetic field, a common model of fractional Chern insulators in two-dimensional materials. From the microscopic wave functions, we derive the commutator of its guiding-center coordinates, set by a many-body Berry curvature that governs its wave packets. A modulation with two flux quanta per unit cell splits the quasihole band into bands with Chern numbers $6$ and $-3$; such opposite signs are generic as long as a weak modulation opens a gap between the anyon bands. In the $C=-3$ band, the quasihole drifts against $\mathbf{E}\times\mathbf{B}$, although the magnetic field has the same sign everywhere. Perturbation theory in the modulation explains these results, and large-scale Monte Carlo calculations confirm them. Anyon bands thus acquire their own topology, which controls anyon motion and may shape the phases of itinerant anyons.