Higher-order Dirac sonic crystals

Abstract Discovering new topological phases of matter is a major theme in fundamental physics and materials science1,2. Dirac semimetal features isolated fourfold linear band crossings, i.e., Dirac points, and provides an exceptional platform for exploring topological phase transitions under symmetry breaking3. Recent theoretical studies4,5 have revealed that a three-dimensional Dirac semimetal can harbor fascinating hinge states, a high-order (HO) topological manifestation not known before. However, realization of such a HO Dirac phase in experiment is yet to be achieved, not to mention the fascinating hinge states, although candidate solid-state materials have been suggested5. Here we propose a minimum model to construct a spinless HO Dirac semimetal protected by C_6v symmetry. By breaking different symmetries, this parent phase transitions into a variety of novel topological phases including HO topological insulator, HO Weyl semimetal, and HO nodal-ring semimetal. Furthermore, for the first time, we experimentally realize this unprecedented HO topological phase in a sonic crystal and unambiguously present the smoking-gun observation of the desired hinge states via momentun-space spectroscopy and real-space visualization. Our findings may offer new opportunities to manipulate classical waves such as sound and light.