Anyonic Chern insulator in graphene induced by surface electromagnon vacuum fluctuations

Abstract

Sub-wavelength cavities have emerged as a promising platform to realize strong light-matter coupling in condensed matter systems. Previous studies are limited to dielectric sub-wavelength cavities, which preserve time-reversal symmetry. Here, we lift this constraint by proposing a cavity system based on magneto-electric materials, which host surface electromagnons with non-orthogonal electric field and magnetic field components. The quantum fluctuations of the surface electromagnons drive a nearby graphene monolayer into an anyonic Chern insulator, characterized by anyonic quasi-particles and a topological gap that decays polynomially with the graphene-substrate distance. Our work opens a path to controllably break time-reversal symmetry and induce exotic quantum states through cavity vacuum fluctuations.

Figures (2)

• Figure 1: (a) Schematic of a magneto-electric sub-wavelength cavity: monolayer graphene sits a distance $l$ above a magneto-electric substrate. Coupling to surface electromagnons opens a topological gap $\Delta_\mathrm{topo}$ at the Dirac points, driving the graphene layer into a Chern insulating state. (b) Electric (red) and magnetic (blue) field profiles for a surface electromagnon mode. The fields are parallel inside the substrate and anti-parallel in vacuum. Furthermore, the fields are confined near the surface, consequently $\Delta_\mathrm{topo}$ grows as $l$ decreases.
• Figure 2: (a) Scaling of the topological gap $\Delta_\mathrm{topo}$ with the graphene-substrate distance $l$, for $v_F = 10^6$ m/s and $\omega_s = 1$ THz. The solid blue line shows the exact result of Eq. (\ref{['eq_mz']}), the dotted blue lines show the $l\rightarrow 0$ and $l\rightarrow \infty$ asymptotic forms discussed in the main text, and the dotted red line illustrates the expected behavior of a proximity-induced effect with exponential decay. (b) Magnitude of the topological gap $\Delta_\mathrm{topo}$ as a function of $\alpha_\mathrm{EM}$ and the surface electromagnon frequency $\omega_s$, with $v_F=10^6$ m/s and $l=3\mathrm{\AA}$. (c) Single-particle Hall conductance $\sigma_{xy}$ as a function of chemical potential $\mu$ at various temperatures.