Abstract
Three-dimensional (3D) gapless topological phases can be classified by the dimensionality of the band degeneracies, including zero-dimensional (0D) nodal points, one-dimensional (1D) nodal lines, and two-dimensional (2D) nodal surfaces. Both nodal points and nodal lines have been realized recently in photonics and acoustics. However, a nodal surface has never been observed in any classical-wave system. Here, we report on the experimental observation of a twofold symmetry-enforced nodal surface in a 3D chiral acoustic crystal. In particular, the demonstrated nodal surface carries a topological charge of 2, constituting the first realization of a higher-dimensional topologically-charged band degeneracy. Using direct acoustic field measurements, we observe the projected nodal surface and its Fermi-arc-like surface states and demonstrate topologically-induced robustness of the surface states against disorders. This discovery of a higher-dimensional topologically-charged band degeneracy paves the way toward further explorations of the physics and applications of new topological semimetal phases.
Highlights
Three-dimensional (3D) gapless topological phases can be classified by the dimensionality of the band degeneracies, including zero-dimensional (0D) nodal points, one-dimensional (1D) nodal lines, and two-dimensional (2D) nodal surfaces
Weyl photonic/acoustic crystals[16,17,18,19,20,21,22], for example, host twofold zero-dimensional (0D) point degeneracies known as Weyl points which are monopoles of quantized Berry flux in three-dimensional (3D) momentum space and carry topological charge ±1; when projected to a surface, two oppositely charged Weyl points are connected in momentum space by open surface-state arcs
Researchers have demonstrated photonic/acoustic crystals with topological nodal lines—band degeneracies lying along one-dimensional (1D) curves in momentum space—which are associated with Berry phase winding of π and drumhead surface states[23,24,25,26]
Summary
Three-dimensional (3D) gapless topological phases can be classified by the dimensionality of the band degeneracies, including zero-dimensional (0D) nodal points, one-dimensional (1D) nodal lines, and two-dimensional (2D) nodal surfaces. Researchers have demonstrated photonic/acoustic crystals with topological nodal lines—band degeneracies lying along one-dimensional (1D) curves in momentum space—which are associated with Berry phase winding of π and drumhead surface states[23,24,25,26].
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