Probing spatially resolved spin density correlations with trapped excitons

TL;DR

This paper proposes a novel optical method using trapped excitons in moiré lattices to spatially resolve electron spin density correlations in 2D materials, enabling the study of quantum phases.

Contribution

It introduces a new spectroscopic technique leveraging exciton-electron interactions to probe spin correlations and quantum phase transitions in 2D layered materials.

Findings

Energy shifts in exciton spectra reveal spin density correlations.

The method can detect quantum phase transitions in 2D magnetic systems.

Probing pairing symmetries in superconducting phases is possible.

Abstract

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 moir\'e 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 moir\'e 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.