Abstract
We propose a one-dimensional Floquet ladder that possesses two distinct topological transport channels with opposite directionality. The transport channels occur due to a Z2 non-Hermitian Floquet topological phase that is protected by time-reversal symmetry. The signatures of this phase are two pairs of Kramers degenerate Floquet quasienergy bands that are separated by an imaginary gap. We discuss how the Floquet ladder can be implemented in a photonic waveguide lattice and show that the direction of transport in the resulting waveguide structure can be externally controlled by focusing two light beams into adjacent waveguides. The relative phase between the two light beams selects which of the two transport channels is predominantly populated, while the angles of incidence of the two light beams determine which of the transport channels is suppressed by non-Hermitian losses. We identify the optimal lattice parameters for the external control of transport and demonstrate the robustness of this mechanism against disorder.
Highlights
The key feature of topological insulators is the existence of robust transport at the boundary, which is protected by the nontrivial topology of the bulk
Non-trivial topology can emerge through the electromagnetic interaction of the Bloch electrons with external or internal gauge fields4–6 and through Kramers degeneracy that is induced by fermionic time-reversal symmetry of the spin 1/2 of the electrons
We have shown that the one-dimensional Floquet ladder introduced in this work provides a promising platform for the external control of the direction of topological transport
Summary
The key feature of topological insulators is the existence of robust transport at the boundary, which is protected by the nontrivial topology of the bulk. In solids, non-trivial topology can emerge through the electromagnetic interaction of the Bloch electrons with external or internal gauge fields and through Kramers degeneracy that is induced by fermionic time-reversal symmetry of the spin 1/2 of the electrons. Naïvely, one would not expect that a photonic system is a suitable platform for topological insulators since photons are neutral bosons. Two waveguides that form a rung of the ladder (indicated by the green ellipses) are simultaneously excited by two light beams that have the same intensity ∣ψ0∣2, but a variable relative phase φ. This initial excitation populates both the left-moving and right-moving transport channel in the waveguide lattice. Our Floquet ladder hosts a Z2 topological phase that exclusively occurs in a non-Hermitian time-reversal symmetric Floquet system. Before we specify the relevant Floquet protocol, let us explain why both non-Hermiticity and time-reversal symmetry are necessary to control the direction of topological transport in a one-dimensional chain
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