Topological strong-field physics on sub-laser-cycle timescale

The sub-laser-cycle timescale of the electronic response to strong fields enables attosecond dynamical imaging in atoms, molecules and solids 1 – 4 , with optical tunnelling and high-harmonic generation the hallmarks of attosecond optical spectroscopy 2 , 5 – 7 . Topological insulators are intimately linked with electron dynamics, as manifested via the chiral edge currents 8 , but it is unclear if and how topology leaves its mark on optical tunnelling and sub-cycle electronic response. Here, we identify distinct bulk topological effects on directionality and timing of currents arising during electron injection into conduction bands. We show that electrons tunnel differently in trivial and topological insulators, 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 and helicities of emitted harmonics that record the phase diagram of the system. Our findings create new roadmaps in studies of topological systems, building on the ubiquitous properties of the sub-laser-cycle strong-field response—a unique mark of attosecond science. Responses to high-intensity mid-infrared laser light are theoretically investigated in the Haldane system. It is found that the primary electronic response, optical tunnelling and high-harmonic emission are sensitive to the topological phase of matter.