Higher-order topological phases of matter, including insulators and semimetals, have attracted much attention, since they can induce novel multidimensional topological boundary states. Recently, a two-dimensional (2D) multipole chiral-symmetric higher-order topological insulator (MCTI) with multipole corner states, protected by multiple chiral numbers (MCNs), has been proposed theoretically and soon will be implemented in circuit and acoustic systems. However, the chiral-symmetry higher-order topological semimetals remain unexplored. In this work, we study the multipole chiral symmetry on the three-dimensional topological semimetals based on long-range hoppings. We theoretically propose two types of multiple chiral topological semimetals (MCTSs). The multipole hinge states, which are protected by $k_z$-dependent MCNs, are observed at one-dimensional (1D) hinge boundaries in the corresponding subspace. To verify our theory, we construct one type of MCTS in acoustic crystal as an example. Four groups of topological hinge states are obtained at each 1D hinge boundary of the constructed acoustic system. These multiple hinge states may have potential applications to improve the sensing and calculation of quantum devices.

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• Phononic crystals
• Topological insulators
• Topological phases of matter
• Semimetals
• First-principles calculations
• Tight-binding model