Bandgap modulations are pivotal for semiconductor-based applications, typically achieved through permanent modifications of material composition or size. Recently, ultrafast dynamic bandgap modulations have been demonstrated in transition metal dichalcogenides (TMDs), leveraging the valley exclusive optical Stark (OS) and Bloch-Siegert (BS) shifts. These effects, which scale linearly with intensity, produce distinct outcomes depending on the excitation polarization. Whereas circular polarization deterministically induces an energy imbalance between the intrinsically degenerate but non-equivalent valleys at the ±K points of the Brillouin zone, linear polarization induces instead equal energy shifts in the ±K valleys. Both, symmetrical and asymmetrical, bandgap shifts in TMDs offer promising opportunities for novel signal modulation schemes or valleytronics applications. However, analysing these effects and quantifying the associated energy shifts usually requires sophisticated two-colour pump-probe techniques.

In this seminar talk, I will present two simplified approaches based on nonlinear optics, particularly second-harmonic generation (SH), to probe valley imbalances and ultrafast bandgap modulations in a tungsten diselenide monolayer.

First, I will demonstrate how valley imbalances can be probed on ultrafast timescales by comparing SH intensities for circularly and linearly polarized fundamental beams (FB). Through numerical and analytical solutions of the semiconductor Bloch equations, we show that a two-photon resonant circularly polarized FB interacts exclusively with the ±K valleys, probing their C3h wave vector group. In contrast, a linearly polarized FB probes the D3h group of the Γ point. This distinction between wave vector groups fully explains the experimentally observed deviation from the expected 2:1 ratio of SH intensities for circular versus linear polarization. 

Second, I will discuss power-dependent SH measurements using linearly polarized excitation, preserving the energy degeneracy in the ±K valleys. Here, the FB equally modifies the optical bandgap via OS/BS shifts, resulting in enhanced or reduced SH signals depending on the detuning Eg−2ℏωFB. In this case, we can extract intensity-induced changes in the nonlinear susceptibility to monitor ultrafast bandgap modulations. These experimental results are again fully supported by our analytical model, which also enables the extraction of key material parameters, including the transition dipole moment and dephasing time.