Ultrafast {\mu}eV-Precision Bandgap Engineering in Low-Dimensional Topological Insulators

Precise and ultrafast control of electronic band structures is a central challenge for advancing quantum functional materials and devices. Conventional approaches--such as chemical doping, lattice strain, or external gating--offer robust stability but remain confined to the quasi-static regime, far from the intrinsic femto- to picosecond dynamics that govern many-body interactions. Here, using cryogenic transient reflectance spectroscopy, we realize dynamic bandgap engineering in the anisotropic topological insulator $\alpha$-Bi$_4$Br$_4$ with unprecedented micro-electron-volt ($\mu$eV) precision. The exceptional sensitivity arises from the cooperative action of long-lived topological carriers, stabilized by restricted bulk-to-edge scattering phase space, together with symmetry-resolved coherent phonons that modulate inter-chain hopping. These channels jointly modify Coulomb screening and interband transitions, enabling both gradual and oscillatory control of the electronic structure. Supported by first-principles and tight-binding theory, we further demonstrate a dual-pump coherent control strategy for continuous, mode-selective tuning of electronic energies with $\mu$eV accuracy. This framework paves the way for ultrafast on-demand band-structure engineering, pointing toward new frontiers in quantum optoelectronics, precision measurement in molecular and biological systems, and attosecond control of matter.