Abstract
Three-dimensional (3D) Weyl and Dirac semimetals garner considerable attention in condensed matter physics due to the exploration of entirely new topological phases and related unconventional surface states. Nodal line and ring semimetals, on the other hand, can facilitate 3D band crossings characterized by nontrivial links such as coupled chains and knots that are protected by the underlying crystal symmetry. Experimental complexities and detrimental effects of the spin-orbit interaction, among others, pose great challenges for the advancement that can be overcome with other systems such as bosonic lattices. Here we demonstrate that a 3D mechanical metamaterial made of granular beads hosts multiple intersecting nodal rings in the ultrasonic regime. By unveiling these yet unseen classical topological phases, we discuss the resilience of the associated novel surface states that appear entirely unaffected to the type of crystal termination, making them a promising platform in ultrasonic devices for non-destructive testing and material characterization.
Highlights
Three-dimensional (3D) Weyl and Dirac semimetals garner considerable attention in condensed matter physics due to the exploration of entirely new topological phases and related unconventional surface states
This active frontier in condensed matter physics recently explored topologically protected degeneracies in Dirac and Weyl semimetals that are identified by topologically robust band-touching manifolds. These unconventional fermionic semimetals are characterized by nontrivial band touching in the form of zerodimensional discrete points, one-dimensional nodal rings and lines, or two-dimensional nodal surfaces
Given the complexity of electronic systems to unveil Weyl and Dirac semimetal physics as well as those peculiar intersecting nodal rings, man-made bosonic system have become increasingly popular to explore in the waves based context, the existence of Dirac-like plasmons[21], optical Weyl points and Fermi arcs[22,23], hourglass nodal lines[24], metallic mesh nodal chains[25], and phononic nodal rings[26]
Summary
Three-dimensional (3D) Weyl and Dirac semimetals garner considerable attention in condensed matter physics due to the exploration of entirely new topological phases and related unconventional surface states. This active frontier in condensed matter physics recently explored topologically protected degeneracies in Dirac and Weyl semimetals that are identified by topologically robust band-touching manifolds These unconventional fermionic semimetals are characterized by nontrivial band touching in the form of zerodimensional discrete points, one-dimensional nodal rings and lines, or two-dimensional nodal surfaces. A vast amount of theory has been devoted to this frontier in Heusler compounds, alkaline earth metals and electrides[7,10,11,12,13,14,15], whereupon experimental verifications of nodal rings have already been observed in non-centrosymmetric superconducting compounds and zirconium-based structures[16,17,18,19] Bosonic settings such as photonic, phononic, and sonic crystals are widely studied with the aim to tailor classical wave properties[20]. Given the complexity of electronic systems to unveil Weyl and Dirac semimetal physics as well as those peculiar intersecting nodal rings, man-made bosonic system have become increasingly popular to explore in the waves based context, the existence of Dirac-like plasmons[21], optical Weyl points and Fermi arcs[22,23], hourglass nodal lines[24], metallic mesh nodal chains[25], and phononic nodal rings[26]
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