Double dual-nodal-line semimetals with large surface density of states: Topological quantum catalysts for the hydrogen-evolution reaction

Topological quantum catalysts are developing rapidly due to the emergence of exotic quantum materials and their corresponding catalytic performance. Although tens of thousands of topological semimetals have been developed, their low topological surface density of states (DOSs) remains a hindrance to the development of high-performance catalysts for electrochemical hydrogen evolution reactions (HERs). In this work, we investigate the potential of double dual-nodal line (DDNL) semimetals, which exhibit large surface DOSs and fair-low Gibbs free energies, as ideal topological quantum catalysts (TQCs) for HER. Using the $\mathrm{Na}\mathrm{Al}\mathrm{Ge}$ compound as a representative example, we demonstrate that its DDNLs and high surface DOSs around the Fermi level provide advantages for achieving exceptionally high catalytic activity in the electrochemical HER process. Through a comparison of catalytic performance under different (electron and hole) doping and uniaxial strain conditions, we establish a linear correlation between the Gibbs free energy ($\mathrm{\ensuremath{\Delta}}{G}_{{\mathrm{H}}^{\ensuremath{\ast}}}$) and the projected surface DOSs on the (001) semi-infinite surface of the DDNL semimetal $\mathrm{Na}\mathrm{Al}\mathrm{Ge}$, specifically for the hydrogen evolution process. Our work introduces an alternative category of high-performance TQCs free of noble metals and contributes to a better understanding of the relationship between catalytic performance for HER and surface DOSs in DDNL semimetals.