Fig. 2
Characterization of instability. a Complex energy of the edge eigenmodes (cf. Eq. (3)). The real part (frequency) is plotted in blue, whereas the imaginary part (amplification) is shown in yellow. The perfectly matching grey curve is the theory Eq. (3) with \({\cal{E}} = g_kE_0 = |{\mathbf{E}}_0||\widetilde {\mathbf{Q}}_{\bar s\bar s}(\pi )| = 4 \times 10^{ - 4}J\) and \(\omega _\pi ^{\prime\prime} \simeq 0.3605J\) (numerically extracted from band structure, not fitted to instability). Note that the excellent agreement only holds if the polarization of the electric field points along y, i.e., along the width of the strip, as we explain in more detail in Supplementary Note 4. b The steady-state edge occupation calculated from Eq. (8) with the same parameters as in Fig. 1 and nonlinear damping η = 10−5J (the same in microscopic theory and chiral waveguide model). Shown in blue is the chiral waveguide model, the yellow dots are calculated numerically from the microscopic Hamiltonian. Parameters are as in Fig. 1, but with W = 15
