Absence of a Superradiant Phase Transition in Dirac Landau Polaritons

One of the most striking predictions in cavity quantum electrodynamics is the condensation of photons into a macroscopically populated ground state, the so-called superradiant phase transition (SRPT). SRPTs are theorized to occur in light-matter coupled systems above a critical coupling strength, yet have not been experimentally realized in equilibrium. On the contrary, the very existence of SRPTs has been largely disputed by No-Go theorems. In cavity-coupled electronic systems with Dirac dispersion, the diamagnetic $\vec{A}^2$-term crucial to No-go theorems is not present at leading order, making graphene Landau level transitions ultrastrongly coupled to terahertz cavities good candidates for SRPTs. In this work, we present the first terahertz spectroscopic measurements of an hBN-encapsulated monolayer graphene flake coupled to a highly sub-wavelength resonator mode. By tuning the graphene carrier density, we drive the resulting Landau polaritons into the ultrastrong coupling regime, with the normalized coupling reaching $\approx 40 \%$, approaching criticality. In this regime, the continuous SRPT would lead to a unique spectroscopic polariton softening, which we consistently rule out. The full polariton dispersion is instead quantitatively reproduced by a Hopfield Hamiltonian using a quasistatic near-field model that accounts for the sub-wavelength character of the cavity.