  Sub-laser cycle time scale of electronic response to strong laser fields
enables attosecond dynamical imaging in atoms, molecules and solids. Optical
tunneling and high harmonic generation are the hallmarks of attosecond imaging
in optical domain, including imaging of phase transitions in solids.
Topological phase transition yields a state of matter intimately linked with
electron dynamics, as manifested via the chiral edge currents in topological
insulators. Does topological state of matter leave its mark on optical
tunneling and sub-cycle electronic response? We identify distinct topological
effects on the directionality and the attosecond timing of currents arising
during electron injection into conduction bands. We show that electrons tunnel
across the band gap differently in trivial and topological phases, for the same
band structure, and identify the key role of the Berry curvature in this
process. These effects map onto topologically-dependent attosecond delays in
high harmonic emission and the helicities of the emitted harmonics, which can
record the phase diagram of the system and its topological invariants. Thus,
the topological state of the system controls its attosecond, highly
non-equilibrium electronic response to strong low-frequency laser fields, in
bulk. Our findings create new roadmaps in studies of topological systems,
building on ubiquitous properties of sub-laser cycle strong field response - a
unique mark of attosecond science.
