Electromagnetic Response of a Half-Filled Chern Band near Topological Criticality

We evaluate electromagnetic-response observables in a half-filled Chern band, across a topological phase transition between a composite Fermi liquid (CFL) and a Fermi liquid (FL) phase. While a sharp gapped plasma mode exists deep in the CFL phase, we demonstrate that it is damped near the proposed continuous phase transition between CFL and FL. This plasmon-damping phenomenon originates from emergent gauge fields and a Dirac-fermion-like spectrum. Similar features also occur in other continuous deconfined topological phase transitions, such as the Laughlin to superfluid transition in a bosonic system. In particular, this damping behavior extends over a finite range across the phase boundary, and, hence, we expect it to persist even when the transition is weakly first order. Furthermore, we analyze the characteristic conductivity behavior, such as the Drude weight, the wave-vector-dependent conductivity, the chiral mirror effect, and thermodynamic behavior, including compressibility and magnetic susceptibility across these topological phase transitions.