Ultrafast and Strong-Field Physics in Graphene-Like Crystals: Bloch Band Topology and High-Harmonic Generation

The emerging possibilities to steer and control electronic motion on subcycle time scales with strong electric fields enable studying the nonperturbative optical response and Bloch bands' topological properties, originated from Berry's trilogy: connection, curvature, and phase. This letter introduces a theoretical framework for the nonperturbative electron dynamics in two-dimensional (2D) crystalline solids induced by the few-cycle and strong-field optical lasers. In the presented model, the expression associated with the Bloch band topology and broken crystal symmetry merges self-consistently in the system observables such as High Harmonic Generation (HHG). This singles out our work from recent HHG calculations from the strongly-driven systems. Concisely, in our theoretical experiment on 2D materials in the strong-field optical regime, we show that Bloch band topology and broken symmetry manifest themselves in several ways: the momentum-resolved attosecond interferometry of electron wave packets, anomalous and chiral velocity in both intraband and interband dynamics, anomalous Hall current and respective HHG highly sensitive to the laser waveform, multiple plateau-cutoff structures in both longitudinal and transverse HHG, the formation of even harmonics in the perpendicular polarization with respect to the driving laser, singular jumps across the phase diagram of the HHG, attosecond chirp, and ultrafast valley polarization induced by the chiral gauge field that is robust to lattice imperfections and scattering. The link between HHG and solid-state band geometry offers an all-optical reconstruction of electron band structure by optical means, and accelerates studies on the non-equilibrium Floquet engineering, topologically-protected nonlinear spin and edge currents, valleytronics, quantum computing and high-temperature superconductivity on sub-femtosecond time scales.