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Research on topological physics of phonons has attracted enormous interest but demands appropriate model materials. Our ab initio calculations identify silicon as an ideal candidate material containing extraordinarily rich topological phonon states. In silicon, we identify various topological nodal lines characterized by quantized Berry phase π, which gives drumhead surface states observable from any surface orientations. Remarkably, a novel type of topological nexus phonon is discovered which is featured by double Fermi-arc-like surface states but requires neither inversion nor time-reversal symmetry breaking. Versatile topological states can be created from the nexus phonons, such as Hopf nodal links by strain. Furthermore, we generalize the symmetry analysis to other centrosymmetric systems and find numerous candidate materials, demonstrating the ubiquitous existence of topological phonons in solids. These findings open up new opportunities for studying topological phonons in realistic materials and their influence on surface physics.

Three-dimensional (3D) topological Dirac semimetal, when thinned down to 2D few layers, is expected to possess gapped Dirac nodes viaquantum confinement effect and concomitantly display the intriguing quantum spin Hall (QSH) insulator phase. However, the 3D-to-2D crossover and the associated topological phase transition, which is valuable for understanding the topological quantum phases, remain unexplored. Here, we synthesize high-quality Na3Bi thin films with √3 × √3 reconstruction on graphene and systematically characterize their thickness-dependent electronic and topological properties by scanning tunneling microscopy/spectroscopy in combination with first-principles calculations. We demonstrate that Dirac gaps emerge in Na3Bi films, providing spectroscopic evidence of dimensional crossover from a 3D semimetal to a 2D topological insulator. Importantly, the Dirac gaps are revealed to be of sizable magnitudes on three and four monolayers (72 and 65 meV, respectively) with topologically nontrivial edge states. Moreover, the Fermi energy of a Na3Bi film can be tuned viaa certain growth process, thus offering a viable way for achieving charge neutrality in transport. The feasibility of controlling Dirac gap opening and charge neutrality enables realizing intrinsic high-temperature QSH effect in Na3Bi films and achieving potential applications in topological devices.