Jin Zhang’s scientific contributions

Band structure and Dirac degeneracy are essential features of sonic crystals/acoustic metamaterials to achieve advanced control of exciting wave effects. In this work, we explore a deep learning approach for the design of phononic crystals with desired dispersion. A plane wave expansion method is utilized to establish the dataset relation between the structural parameters and the energy band features. Subsequently, a multilayer perceptron model trained using the dataset can yield accurate predictions of wave behavior. Based on the trained model, we further impose a re-learning process around a targeted frequency, by which Dirac degeneracy and double Dirac degeneracy can be embedded into the band structures. Our study enables the deep learning approach as a reliable design strategy for Dirac structures/metamaterials, opening up the possibilities for intriguing wave physics associated with Dirac cone.

In recent years, topology has offered an elegant degree of freedom (DOF) for light and sound manipulation. There exists persistent effort to explore the origin of topological phases based on symmetry, while it becomes rather challenging in complex networks or multiple DOF systems where geometric symmetries are not apparent. Here, we demonstrate a linear degeneracy induced by latent mirror symmetry in a zigzag granular chain whose DOF is three times larger than its bead number. An isospectral reduction approach and graphical representation are developed to track the topological origin of the degeneracy. We show how the latent mirror symmetry leads to the degeneracy and how it is manifested in a properly chosen eigenmode space. Moreover, we reveal the existence of topological edge states and their robustness against different disorders when the degeneracy is gapped. Our study takes a pivotal step toward exploiting topological waves in complex networks or disordered systems, opening up the perspective of offering new flexibilities for classical wave tailoring.