Plane-Wave Photon-Fock Cavity QED-DFT: Chiral-Cavity-Induced Topology in Graphene

We develop an explicit plane-wave (PW) times photon-Fock approach to the quantized, velocity-gauge Pauli--Fierz Hamiltonian for periodic, first-principles calculations: because the quantized vector potential is spatially uniform, the light--matter coupling reduces to an operator-valued shift of the crystal momentum, K to K+ /c, and the existing plane-wave machinery of ordinary solid-state DFT is reused essentially unchanged. This PW times Fock construction puts first-principles cavity QED of periodic solids on the same footing as the Fock-space coupled-cluster and configuration-interaction methods already developed for molecules, opening hitherto inaccessible systems---materials in a linear or chiral cavity, in particular---to first-principles plane-wave calculations. We illustrate the method with monolayer graphene in linear and chiral cavities, obtaining a polarization-selective Haldane gap together with the corresponding density-of-states, real-space, and circular-dichroism optical signatures. A full Brillouin-zone Berry-curvature calculation confirms the topological character of the chiral-cavity gap directly: the occupied manifold carries a quantized Chern number that steps through a non-monotonic sequence, C=1 to3 to-1 to1 to2 to-1 to1, with two narrow, sign-reversed windows---a property of extended, vacuum-dressed matter with no counterpart in a finite molecular system.