Tunneling-induced fractal transmission in Valley Hall waveguides

Abstract

The Valley Hall effect provides a popular route to engineer robust waveguides for bosonic excitations such a photons and phonons. The almost complete absence of backscattering in many experiments has its theoretical underpinning in a smooth-envelope approximation that neglects large momentum transfer and is accurate only for small bulk band gaps and/or smooth domain walls. For larger bulk band gaps and hard domain walls backscattering is expected to become significant. Here, we show that in this experimentally relevant regime, the reflection of a wave at a sharp corner becomes highly sensitive on the orientation of the outgoing waveguide relative to the underlying lattice. Enhanced backscattering can be understood as being triggered by resonant tunneling transitions in quasimomentum space. Tracking the resonant tunneling energies as a function of the waveguide orientation reveals a self-repeating fractal pattern that is also imprinted in the density of states and the backscattering rate at a sharp corner.

References in corpus (10)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Observation of topological valley transport of sound in sonic crystals
• Topological confinement in bilayer graphene
• Spectral signatures of many-body localization with interacting photons
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Observation of topological valley modes in an elastic hexagonal lattice
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Observation of Gigahertz Topological Valley Hall Effect in Nanoelectromechanical Phononic Crystals
• Tunneling in the Brillouin Zone: Theory of Backscattering in Valley Hall Edge Channels