  We have observed the Berry phase effect associated with interband coherence
in topological surface states (TSSs) using two-color high-harmonic
spectroscopy. This Berry phase accumulates along the evolution path of strong
field-driven election-hole quasiparticles in electronic bands with strong
spin-orbit coupling. By introducing a secondary weak field, we perturb the
evolution of Dirac fermions in TSSs and thus provide access to the Berry phase.
We observe a significant shift in the oscillation phase of the even-order
harmonics from the spectral interferogram. We reveal that such a modulation
feature is linked to the geometric phase acquired in the nonperturbative
dynamics of TSSs. Furthermore, we show that the overwhelming Berry phase effect
can significantly deform the quantum paths of electron-hole pairs, thus
enhancing the ability to harness electron spin using lightwaves in quantum
materials with strong spin-orbit interactions.
