Direct measurement of optically induced broken time-reversal symmetry in centrosymmetric atomically thin crystals

Time-reversal symmetry (TRS) is one of the most fundamental properties of crystals, connecting the energy dispersion with spin and quantum geometric properties, and underlying non-trivial topology and spin textures [1]. Two-dimensional transition metal dichalcogenides (TMDs) are an ideal model system to study symmetry-related optical and electronic properties in solid state physics, because they allow to independently tune and engineer both TRS and space-inversion symmetry (SIS). SIS depends on the number of layers, where an even/odd number breaks/preserves space-inversion; TRS can be controlled optically on ultrafast timescales via valley-selective bandgap opening. Recently, second harmonic generation has been employed to probe broken TRS in a non-invasive and ultrafast fashion [2]. However, this method remains limited to systems of broken SIS. In this work, we generalize the method towards systems of preserved SIS, by utilizing third harmonic generation. We demonstrate that broken TRS can be directly measured as a rotation of the TH polarization. From this, we extract the ultrafast all-optical TRS breaking by spin-valley and spin-valley-layer selective bandgap modulation in non-centrosymmetric monolayer and centrosymmetric bilayer TMDs, respectively.

[1] C. Bao et al., Nat Rev Phys 4, 33-48 (2022)

[2] P. Herrmann et al., Nat. Photon. 19, 300-306 (2025)