Fig. 4: Observation of PT-related hinge states.
From: Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal
a Experimental sample for measuring the hinge states (HSs). The numbers—label the four y-directional hinges. b Eigen frequencies for the sample shown in a at ky = π/a, obtained from full-wave simulation. The blue dots represent the bulk and surface states, and the red dots indicate the HSs. c, Eigen profiles for the two states highlighted in red in b (∣p∣ denotes the absolute value of acoustic pressure). The color indicates the amplitude of the acoustic pressure. d–g Experimentally measured dispersions for hinge 1 d, hinge 2 e, hinge 3 f, and hinge 4 g. The gray dots represent simulated eigenfrequencies of the bulk and SSs, and the red dots indicate simulated hinge bands. The solid blue lines denote the projections of the nodal rings. h–k Experimentally measured acoustic intensity distributions on two surfaces adjacent to hinge 1 h, hinge 2 i, hinge 3 j, and hinge 4 k. The red star indicates the position of the speaker and the red dashed line highlights the position of the hinge. The operating frequencies of the speaker are chosen as: 3078 Hz (hinge 1 and hinge 3), 3076 Hz (hinge 2) and 3080 Hz (hinge 4), which are around the eigenfrequencies of the HSs.
