Topological chiral edge modes in the continuum of a trivial bulk

Abstract

Chiral edge modes in topological states of matter are routinely found inside band gaps, which may be deformed and shifted as a function of the lattice momentum. Here we show that they can exist inside a bulk band instead, i.e., in the continuum. These chiral edge modes in the continuum (CEMICs) are induced by introducing an imaginary magnetic flux to an otherwise topologically trivial two-dimensional system, realized by imposing asymmetric couplings along the edge. While the stronger couplings provide a preferred circulation direction, we find that the edge localization of CEMICs does \textit{not} originate from the non-Hermitian skin effect, which is typically associated with systems featuring asymmetric couplings and the open boundary condition. Instead, this edge localization is due to the energy exchange between the system and the environment at the asymmetric coupling junctions, which leads to a parity-time (PT) transition in the Brillouin zone. Intriguingly, the onset of CEMICs is independent of the system size in the macroscopic limit, which is given by the golden ratio between the asymmetric couplings and their geometric average.