A Two Dimensional Topological Electron Gas

The two-dimensional electron gas (2DEG) is one of the paradigmatic examples of condensed matter but is fined-tuned in the sense that its Berry curvature exactly vanishes. This talk introduces a 2d topological electron gas (2TEG), a simple model of a band minimum whose potential/kinetic ratio r_s and Berry curvature concentration λ_s are independently tunable. In the limit of vanishing Berry curvature, this model reduces to the standard 2DEG, with a Fermi liquid phase that transitions to a Wigner crystal at sufficiently large r_s. If sufficient Berry curvature is added, the Wigner crystal undergoes a transition to an anomalous Hall crystal (AHC), a phase that spontaneously breaks translation symmetry to crystalize like the Wigner crystal, but also exhibits the integer quantum Hall effect. We will show conditions under which the AHC is stabilized beyond mean-field level, and discuss its first-order and continuous phase transitions. We will conclude by discussing its experimental relevance for rhombohedral graphene multilayers, where the AHC was originally proposed to explain the appearence of fractional quantum anomalous Hall effects.