Probing spatially resolved spin density correlations with trapped excitons

The rapidly growing class of atomically thin and tunable van der Waals materials is intensely investigated both in the context of fundamental science and for new technologies. There is in this connection a widespread need for new ways to probe the electronic properties of these layered materials, since their two-dimensional (2D) character make conventional probes less efficient. Here, we show how excitons trapped in a moiré lattice can be used as an optical probe for spatially resolved electron spin density correlations in such materials. The electrons in the material of interest virtually tunnel to the moiré lattice where they scatter on the excitons after which they tunnel back. This gives rise to an effective spin-dependent and spatially localised potential felt by the electrons, which in turn leads to energy shifts that can be measured spectroscopically in the exciton spectrum. Using second order perturbation theory combined with a solution to the exciton-electron scattering problem, we show that the electrons mediate an interaction between two excitons resulting in an energy shift proportional to their two-point spin density-density correlation function evaluated at the exciton positions. We then discuss two specific applications of our setup. First, we show that quantum phase transitions between different in-plane anti-ferromagnetic orders in a 2D lattice give rise to large and measurable shifts in the exciton spectrum in the critical regions. Second, we analyse how different pairing symmetries of superconducting phases can be probed. This demonstrates that our scheme opens up new ways to probe electron spin density correlations, which is a key property of many quantum phases predicted to exist in the new 2D materials.

💡 Research Summary

The manuscript presents a novel, all‑optical method for probing spatially resolved spin‑density correlations in two‑dimensional (2D) quantum materials. The authors consider a heterostructure consisting of two vertically stacked 2D layers separated by an insulating spacer (e.g., hBN). In the upper layer a deep moiré potential traps two excitons at well‑defined positions r₁ and r₂; the lower layer hosts the electronic system whose spin correlations are to be measured. Electrons (or holes) in the lower layer can virtually tunnel into the upper layer with amplitude t⊥, scatter off the trapped excitons, and tunnel back. Because the exciton‑electron interaction is strongly spin selective (only opposite‑spin scattering supports a bound trion state), the scattering process generates an effective, spin‑dependent static potential for the lower‑layer electrons: \