Inverse Design of Valley-Like Edge States of Sound Degenerated Away from the High-Symmetry Points in a Square Lattice

Jishi Yang; Yaolu Liu; Dongyang Sun; Ning Hu; Huiming Ning

doi:10.3390/ma15196697

Inverse Design of Valley-Like Edge States of Sound Degenerated Away from the High-Symmetry Points in a Square Lattice

Materials (Basel). 2022 Sep 27;15(19):6697. doi: 10.3390/ma15196697.

Authors

Jishi Yang¹, Yaolu Liu¹, Dongyang Sun², Ning Hu^{1

3}, Huiming Ning¹

Affiliations

¹ College of Aerospace Engineering, Chongqing University, Chongqing 400044, China.
² Nanjing Research Institute, Chongqing University, Nanjing 211800, China.
³ School of Mechanical Engineering, and National Engineering Research Center for Technological Innovation Method and Tool, Hebei University of Technology, Tianjin 300401, China.

Abstract

Robust edge states of periodic crystals with Dirac points fixed at the corners or centers of the Brillouin zones have drawn extensive attention. Recently, researchers have observed a special edge state associated with Dirac cones degenerated at the high symmetric boundaries of the first irreducible Brillouin zone. These nodal points, characterized by vortex structures in the momentum space, are attributed to the unavailable band crossing protected by mirror symmetry. By breaking the time reversal symmetry with intuitive rotations, valley-like states can be observed in a pair of inequivalent insulators. In this paper, an improved direct inverse design method is first applied to realize the valley-like states. Compared with the conventional strategy, the preparation of transition structures with degeneracy points is skipped. By introducing the quantitative gauge of mode inversion error, insulator pairs are directly obtained without manually tuning the structure with Dirac cone features.

Keywords: edge states; explicit geometry description; inverse design; valley-like states.

Grants and funding

This work was supported by the Chinese National Natural Science Fund (Grant No.: U1864208), National Science and Technology Major Project (2017-VII-0011-0106), Science and Technology Planning Project of Tianjin (20ZYJDJC00030), the Key Program of Research and Development of Hebei Province (202030507040009), the Fund for Innovative Research Groups of Natural Science Foundation of Hebei Province (A2020202002) and the Key Project of Natural Science Foundation of Tianjin (S20ZDF077).