Probing Majorana wavefunctions in Kitaev honeycomb spin liquids with second-order two-dimensional spectroscopy*

Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable tool to probe the nature, couplings, and lifetimes of excitations in quantum materials. It thus promises to identify unique signatures of spin liquid states in quantum magnets by directly probing the properties of their exotic fractionalized excitations. Here, we calculate the second-order 2DCS of the Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints appear already in this lowest-order nonlinear response χ⁽²⁾_yzx(ω₁,ω₂) when using crossed light polarizations. We further relate the off-diagonal 2DCS peaks to the localized nature of the matter Majorana excitations trapped by Z₂ flux excitations and show that 2DCS thus directly probes the inverse participation ratio of Majorana wavefunctions. By providing experimentally observable features of spin liquid states in the 2D spectrum, our work can guide future 2DCS experiments on Kitaev magnets.