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Motivated by the novel properties of topological nodal-line semimetal and its compatibility with the well-developed Si-based semiconductor technology, we propose a three-dimensional all-silicon topological nodal-line semimetal composed of interpenetrating silicene networks (ISN). Using state-of-the-art first-principles calculations and the cluster expansion method, we find the ISN structure to be dynamically, thermally, and mechanically stable. In addition, it exhibits linearly dispersive band crossings along two perpendicular high-symmetry directions due to the band inversion and shows two nontrivial nodal lines, traversing in the Brillouin zone near the Fermi level. Furthermore, ISN has the potential as an anode material for sodium-ion batteries with an extremely low diffusion energy barrier and a small volume change during the charging/discharging process, which would lead to a high rate and stable cycling performance.

It has been a great challenge to develop a high-rate anode material with high-capacity, fast Li-ions diffusion and long cycling life going beyond the commercially used graphite in Li-ion battery. Here for the first time we propose a strategy combined high-pressure synthesis method with the global structure search to find a topological semimetal porous carbon as the desired anode. Our crystal-structure searching shows that we can obtain the ground state of an orthorhombic phase $\mathrm{Li}{\mathrm{C}}_{6}$ with regular pores at 30 GPa, and when the Li atoms are removed, the resulting carbon structure is the recently predicted interlocked graphene network (IGN) that is a topological semimetal with an intrinsic high electronic conductivity. Based on the state-of-the-art first-principles calculations, we further find that the Li-ion migration energy barrier in the IGN is extremely low and the estimated diffusion coefficient can reach a magnitude of ${10}^{\ensuremath{-}4}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}/\mathrm{s}$ at both low and high Li concentrations, which is three orders of magnitude larger than that of graphite anode. Moreover, the volume changes during the Li insertion and deinsertion are smaller than $3.2%$, while the theoretical specific capacity is the same as that of graphite anode. Our studies not only suggest a practical way of synthesizing the topological semimetal carbon but also propose a new anode material for Li-ion battery.