Resolving self-cavity effects in two-dimensional quantum materials

Two-dimensional materials and van der Waals (vdW) heterostructures host many strongly correlated and topological quantum phases on the $\sim$ meV energy scale. Direct electrodynamical signatures of such states are thus expected to appear in the terahertz (THz) frequency range (1 THz $\sim$ 4 meV). Because the typical size of vdW heterostructures ($\sim$10 $\mu m$) is much smaller than the diffraction limit of THz light, probing THz optical conductivities necessitates the use of near-field optical probes. However, interpreting the response of such near-field probes is complicated by finite-size effects, the presence of electrostatic gates, and the influence of the probe itself on material dynamics -- all of which conspire to form polaritonic self-cavities, in which interactions between THz electromagnetic fields and material excitations form discretized standing waves. In this paper, we demonstrate the relevance of self-cavity effects in 2D materials and derive an analytical framework to resolve these effects using the emerging experimental technique of time-domain on-chip THz spectroscopy. We show that by pairing experiments with the analytical theory, it is possible to extract the THz conductivity and resolve collective mode dynamics far outside the light cone, with $\sim \mu m$ in-plane and $\sim nm$ out-of-plane resolution. This study lays the groundwork for studying quantum phases and cavity effects in vdW heterostructures and 2D quantum materials.