Fig. 3: Dynamic transfer of chiral edge states via anti-parity-time (APT) phase transition.

a Schematic illustration of a modulated type-II hyperbolic Chern insulator for implementing an effective two-level anti-parity-time symmetric (APT-S) model. b Eigenenergy of the system in a as a function of the modulation strength ρ, where the color indicates the power flow β of each eigenstate. c β as a function of κ. The solid lines (dots) are analytic (numerical) results calculated from the APT Hamiltonian \({H}_{{APT}}\) (tight-binding model calculations). Pink and blue regions denote the anti-parity-time-symmetry-broken (APT-B) and APT-S phase, respectively. The yellow star represents an APT exceptional point (EP). d Intensity distributions of quasi-EP eigenstates marked by yellow stars in b and c. e Wave packet transmissions of outer-outer (\({S}_{21}\)) and outer-inner (\({S}_{31}\)) edge transports as a function of ρ. Inset illustrates that a wave packet excited by an outer edge source (green star), is splitted into two wave packets by the channel, which are detected by outer (blue dot) and inner (red dot) edge probes. f Instantaneous intensity distributions of wave-packet at time 40, 84, 104, and 292, respectively, for ρ = 100 marked by yellow dashed line in e.