Finite temperature electric field induced two-dimensional coherent nonlinear spectroscopy in a Kitaev magnet

We study electric field induced two-dimensional coherent nonlinear optical spectroscopy (2DCS) in a Kitaev magnet at finite temperature. We show that 2DCS is susceptible to both types of fractional quasiparticles of this quantum spin-liquid, i.e., fermions and flux visons. Focusing on the second order response, we find a strong antidiagonal feature in the two-dimensional frequency plane, related to the galvanoelectric effect of the fractional fermions. Perpendicular to the antidiagonal, the width of this feature is set by quasiparticle relaxation rates beyond the bare Kitaev magnet, thereby providing access to single-particle characteristics within the multi-particle 2DCS continuum. While the structure of the 2DCS susceptibility stems from the fermionic quasiparticles and displays Fermi blocking versus temperature, the emergent bond randomness which arises due to thermally populated visons strongly modifies the fermionic spectrum. Therefore also the presence of gauge excitations is manifest in the 2DCS susceptibility as the temperature is increased beyond the flux proliferation crossover. Our results are consistent with and extend previous findings on second harmonic generation in Kitaev magnets.