Cavity quantum electrodynamical Chern insulator: Towards light-induced quantized anomalous Hall effect in graphene

We show that an energy gap is induced in graphene by light-matter coupling to a circularly polarized photon mode in a cavity. Using many-body perturbation theory, we compute the electronic spectra which exhibit photon-dressed sidebands akin to Floquet sidebands for laser-driven materials. In contrast with Floquet topological insulators, in which a strictly quantized Hall response is induced by light only for off-resonant driving in the high-frequency limit, the photon-dressed Dirac fermions in the cavity show a quantized Hall response characterized by an integer Chern number. Specifically for graphene, we predict that a Hall conductance of $2e^2/h$ can be induced in the low-temperature limit.

Figure 1

Two-dimensional (2D) material inside a chiral cavity. (a) Setup for 2D graphene between cavity mirrors a distance $\lambda /2$ apart, where $\lambda$ is the wavelength of the fundamental cavity photon mode. The red spiral indicates the circular photon polarization. The 2D material is encapsulated in a dielectric medium (glassy region). (b) Dirac cone of a 2D Dirac material at electron-photon coupling $g=0$. (c) Energy gap $\mathrm{\Delta }$ due to time-reversal symmetry breaking for $g>0$.

Figure 2

Electronic spectral function in circularly polarized cavity. (a) Spectral intensity $A(k,\epsilon )$ versus momentum $k$ and binding energy $\epsilon$ for temperature $T=4.2\mathrm{K}$ and cavity frequency $\omega =0.3\mathrm{eV}$ for coupling strength $g=0.023\mathrm{eV}$. (b) Line cut of the spectral intensity $A(k,\epsilon )$ at the Dirac point $k=0$ for the same parameters as in (a) on a logarithmic scale. Colored lines show the occupied part of the spectrum at different temperatures.

Figure 3

Spectral function showing sidebands for varying coupling strength. (Left) Spectral intensity $A(k,\epsilon )$ (Dirac point) for temperature $T=1.0\mathrm{K}$ and cavity frequency $\omega =0.3\mathrm{eV}$ at coupling strength $g=0.069\mathrm{eV}$. (Middle, right) Same as in left panel but for increased coupling strengths $g=0.069$ and 0.23 eV, respectively.

Figure 4

Hall conductance for different cavity frequencies. Hall conductance as a function of temperature for cavity photon frequencies as indicated.