λ‑Jellium and Effective‑Field Theory of Topological Electron Crystals

Two dimensional crystals that breaks continuous translation symmetry can be characterized by two invariants: the charge density at zero magnetic field, and the Hall conductance. Crystals with nonzero Hall conductance are called Hall crystals, and they intertwine nontrivial topology with spontaneous symmetry breaking. Recent advances in two-dimensional materials with rich array of nontrivial topological phases have generated new interest in Hall crystals.

In this talk, I will first show a simple topological constrain on the current of topological crystals. In the presence of nonzero magnetic field and nonzero conductance, charges get bound to magnetic flux. We show that these charges are immobile, and gives a topological correction to the amount of current.

Next, I introduce a simple model, lambda-jellium. The low energy band in this model has nonzero Berry curvature, that can seed an anomalous Hall crystal (AHC) phase — Hall crystal at zero magnetic field. We show the rich phase diagram of this model, that supports multiple competing nontrivial phases.

Finally, I will discuss the phonon dynamics of topological crystals by deriving their effective field theory and comparing it against our numerical results.