Spin dependent bandgap renormalization and state filling effect in Bi${}_2$Se${}_3$ observed by ultrafast Kerr rotation

We investigate the ultrafast spin dynamics of the prototypical topological insulator $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ using time-resolved Kerr-rotation (polarization-change) measurements across near-infrared wavelengths. The Kerr-rotation angle $\mathrm{\Delta }{\theta }_K$ of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ was found to significantly depend on photon energy around a resonance transition ($\sim 1.0\mathrm{e}\mathrm{V}$) of bulk states, as well as the ellipticity of the pump light, in the presence of spin excitation. The observed photon-energy dependence of $\mathrm{\Delta }{\theta }_K$ can be well simulated by assuming spin-dependent refractive-index changes in the presence of band-gap renormalization and state-filling effect upon photoexcitation. Our study delivers comprehensive insights into the opto-spintronic properties of bulk $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ and the fundamental physical processes underlying polarization changes. These findings are expected to be crucial in developing ultrafast magneto-optical memory devices, which can perform read-and-write operations in the Terahertz regime.