Neuron-Inspired Steiner Tree Networks for 3D Low-Density Metastructures.

Three-dimensional (3D) micro-and nanostructures have played an important role in topological photonics, microfluidics, acoustic, and mechanical engineering. Incorporating biomimetic geometries into the design of metastructures has created low-density metamaterials with extraordinary physical and photonic properties. However, the use of surface-based biomimetic geometries restricts the freedom to tune the relative density, mechanical strength, and topological phase. The Steiner tree method inspired by the feature of the shortest connection distance in biological neural networks is applied, to create 3D metastructures and, through two-photon nanolithography, neuron-inspired 3D structures with nanoscale features are successfully achieved. Two solutions are presented to the 3D Steiner tree problem: the Steiner tree networks (STNs) and the twisted Steiner tree networks (T-STNs). STNs and T-STNs possess a lower density than surface-based metamaterials and that T-STNs have Young's modulus enhanced by 20% than the STNs. Through the analysis of the space groups and symmetries, a topological nontrivial Dirac-like conical dispersion in the T-STNs is predicted, and the results are based on calculations with true predictive power and readily realizable from microwave to optical frequencies. The neuron-inspired 3D metastructures opens a new space for designing low-density metamaterials and topological photonics with extraordinary properties triggered by a twisting degree-of-freedom.