High-order harmonics from elliptically polarized laser for classification of topological states in 2D Chern insulators and 2D topological insulators.

High-order harmonics (HH) have drawn attention in the field of condensed matter physics mainly because of the capability of light to encode structural, dynamical, and topological information. In this paper, we address the fundamental question whether HH can map topological information in two-dimensional (2D) quantum materials by studying the interaction between topological materials and an elliptically polarized laser. We use the Haldane model for topological Chern insulators (CIs) and the Kane-Mele model for topological insulators (TIs). In the case of a circularly polarized or nearly circularly polarized driving field in CIs and TIs, the harmonic intensity of the co-rotating orders is increased. This increase in topologically non-trivial materials implies that HH can be used to detect topological transitions in 2D CIs and TIs. Moreover, interference between two spin bands in TIs does not affect the elliptical dependence of co-rotating harmonic orders in the plateau region.