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In frequently studied two-band models for solid-state high-harmonic generation, interband harmonics in principle can range from the minimum to the maximum bandgap. However, it is known that a laser-intensity dependent cutoff exists that may be well below the maximum bandgap unless the laser intensity is so high that the electrons explore the entire Brillouin zone. We show that this laser-intensity dependent cutoff is formed by destructive interference of the emission of electrons starting at different initial states in the Brillouin zone. The calculations in this work are for Su-Schrieffer-Heeger chains but our findings apply to other two-band systems as well. Only when the sampling of the Brillouin zone is fine enough or, equivalently, a finite chain is long enough in position space, the destructive interference is complete and forms the cutoff. For coarser sampling and shorter chains all harmonics between minimum and maximum bandgap are emitted. A time-frequency analysis shows how certain trajectories are responsible for the formation of the cutoff., 11 pages, 6 figures

Edge states play a major role in the electron dynamics of topological insulators as they are the only conducting part in such materials. In this work, we consider the Haldane model for a 2D topological insulator, subjected to an intense laser field. We compare the numerically simulated high-harmonic generation (HHG) in the bulk of the Haldane model to HHG in corresponding finite flakes with edge states present, and explain the differences. In particular, peaks for energies below the bulk band gap appear in the spectra for the finite flakes. The positions of these peaks show a strong dependence on the size of the flakes, which can be explained using the dispersion relation for the edge states., 9 pages, 7 figures

The generation of high-order harmonics in finite, hexagonal nanoribbons is simulated. Ribbons with armchair and zig-zag edges are investigated by using a tight-binding approach with only nearest neighbor hopping. By turning an alternating on-site potential off or on, the system describes for example graphene or hexagonal boron nitride, respectively. The incoming laser pulse is linearly polarized along the ribbons. The emitted light has a polarization component parallel to the polarization of the incoming field. The presence or absence of a polarization component perpendicular to the polarization of the incoming field can be explained by the symmetry of the ribbons. Characteristic features in the harmonic spectra for the finite ribbons are analyzed with the help of the band structure for the corresponding periodic systems., Comment: 12 pages, 6 figures

The high-order harmonic generation in finite topological nanoribbons is investigated using a tight-binding description. The ribbons consist of hexagons and are almost one-dimensional. Two edge states emerge at the short edges of the ribbon after a gap closure between valence and conduction band, indicating a topological phase transition. The energies of those edge states as functions of the tight-binding parameters display crossings and avoided crossings, which influence the high-harmonic spectra., Comment: 8 pages, 7 figures

A theory for laser-driven electron dynamics and high-harmonic generation in bulk solids with two lattice sites per unit cell of arbitrary dimension is formulated. In tight-binding approximation, such solids can be described by $2\times 2$ Bloch-Hamiltonians. Our theory is able to fully capture topological effects in high-harmonic generation by such systems because no simplifications beyond tight-binding, dipole approximation, and negligible depletion of the valence band are made. An explicit, analytical expression for the electron velocity is given. Exemplarily, the theory is applied to the Su-Schrieffer-Heeger chain and the Haldane model in strong laser fields., 14 pages, 6 figures, RevTeX

Recent studies in high-harmonic spectroscopy of condensed matter mainly focused on the bulk of the system under consideration. In this work, we investigate the response of thin, hexagonal nanoribbons to an intense laser pulse that is linearly polarized along the ribbon. Such nanoribbons are prime examples of two-dimensional systems that are bulk-like in one direction and finite in the other direction. Despite the atomically thin scale in the direction perpendicular to the linearly polarized driving laser field, the emitted harmonics are elliptically polarized if an alternating onsite potential and Haldane hopping is taken into account. For given hoppings, we find a sudden change of the helicity for a certain harmonic order. The origin of this flip is traced back to phase differences between the components of Bloch states., Comment: 9 pages, 10 Figures, RevTeX

Su-Schrieffer-Heeger (SSH) chains are the simplest model systems that display topological edge states. We calculate high-harmonic spectra of SSH chains that are coupled to an external laser field of a frequency much smaller than the band gap. We find huge differences between the harmonic yield for the two topological phases, similar to recent results obtained with more demanding time-dependent density functional calculations [D. Bauer, K.K. Hansen, Phys. Rev. Lett. 120, 177401 (2018)]. This shows that the tight-binding SSH model captures the essential topological aspects of the laser-chain interaction (while higher harmonics involving higher bands or screening in the metal phase are absent). We study the robustness of the topological difference with respect to disorder, a continuous phase transition in position space, and on-site potentials. Further, we address the question whether the edges need to be illuminated by the laser for the huge difference in the harmonic spectra to be present., Comment: 12 pages, 12 figures, RevTeX4