Satellite Dirac cones in phononic crystals.

Satellite Dirac cones in graphene systems are challenging to observe due to limited momentum-space resolution, hindering further exploration of their bulk-edge correspondence and associated transport properties. Here, we tackle this challenge by simplifying the bilayer configuration into a monolayer one with strong long-range couplings-an arrangement unattainable in natural materials but achievable in artificial structures for classical waves. Using phononic crystals for acoustic waves, we experimentally observe the satellite Dirac cones in the presence of third-nearest neighbor couplings and identify the acoustic edge states determined by their distinct non-trivial winding numbers. The satellite valleys emerge by introducing extra on-site potential, leading to multiple valley interface states. We further identify a frequency window enabling anomalous forward transport of the valley interface states in a standard four-channel splitter. Note that the introduction of long-range couplings is a systematic approach to engineering topological properties. Our findings establish a promising framework for multiple Dirac cones and valleys, opening new avenues for wave manipulation and signal processing in topological materials across both classical and quantum systems.