Modifying the integer quantum Hall effect with cavity vacuum fields

At 50mK sample temperature we measure electron transport in the dark. We immerse a Hallbar into the cavity vacuum fields of a 2-dimensional metamaterial, complementary a split ring resonator resonant in the THz. With this platform, we recently showed that the interaction with vacuum fields not only modifies the finite resistances of the Shubnikov de Haas oscillations in the diffusive transport regime, but it also breaks the topological protection in the integer quantum regime. As a topological insulator, the quantum Hall system is paradigmatic for being robust under the influence of short-range perturbations. We observe the loss of the zero-resistance states in the longitudinal traces and of quantization of the Hall plateaus due to the cavity induced long-range perturbations. The accompanying picture to this long-range perturbation is called "cavity mediated electron hopping". It posits that we can lift an electron occupying the disordered eigenstate Φ_λⁿ from the nth Landau level into the (n+1)th via the absorption of a virtual photon. The inverse process then drops the electron back into the nth Level but into a disordered eigenstate Φ_λ' ⁿ, in a different location. Effectively, with this process electrons can now scatter between the topologically protected edge states via the insulating bulk and break topological protection. We quantitatively characterize this loss of quantization as vacuum field induced resistivity ρ_vac^xx.