All-Silicon Topological Semimetals with Closed Nodal Line

Because of the natural compatibility with current semiconductor industry, silicon allotropes with diverse structural and electronic properties provide promising platforms for next-generation Si-based devices. After screening 230 all-silicon crystals in the zeolite frameworks by first-principles calculations, we disclose two structurally stable Si allotropes (AHT-Si₂₄ and VFI-Si₃₆) containing open channels as topological node-line semimetals with Dirac nodal points forming a nodal loop in the k _z = 0 plane of the Brillouin zone. Interestingly, their nodal loops protected by inversion and time-reversal symmetries are robust against SU(2) symmetry breaking because of the very weak spin-orbit coupling of Si. When the nodal lines are projected onto the (001) surface, flat surface bands can be observed because of the nontrivial topology of the bulk band structures. Our discoveries extend the topological physics to the three-dimensional Si materials, highlighting the possibility of realizing low-cost, nontoxic, and semiconductor-compatible Si-based electronics with topological quantum states.