Nodal-line semimetal states in the positive-electrode material of a lead-acid battery: Lead dioxide family and its derivatives

Based on first-principles calculations and symmetry analysis, we report that the three-dimensional nodal-line (NL) semimetal phases can be realized in the lead dioxide family ( $\ensuremath{\alpha}$ -${\mathrm{PbO}}₂$ and $\ensuremath{\beta}$ -${\mathrm{PbO}}₂$) and its derivatives. The $\ensuremath{\beta}$ -${\mathrm{PbO}}₂$ features two orthogonal nodal rings around the Fermi level, protected by the mirror reflection symmetry. The effective model is developed and the related parameters are given by fitting with the HSE06 band structures. The NLs mainly come from the $p$ orbitals of the light element O and are rather robust against such tiny spin-orbit coupling. The NL phase of the $\ensuremath{\alpha}$ -${\mathrm{PbO}}₂$ can be effectively tailored by strain, making a topological phase transition between a semiconductor phase and a NL phase. In addition, the exploration of $\ensuremath{\beta}$ -${\mathrm{PbO}}₂$ derivatives (i.e., $\ensuremath{\beta}$ -${\mathrm{PbS}}₂$ and $\ensuremath{\beta}$ -${\mathrm{PbSe}}₂$) and confirmation of their topological semimetallicity greatly enrich the NL semimetal family. These findings pave a route for designing topological NL semimetals and spintronic devices based on the realistic ${\mathrm{PbO}}₂$ family.