High-performance hydrogen evolution reaction in quadratic nodal line semimetal Na2CdSn

Abstract

Topological nodal line semimetals (TNLSMs), which exhibit one-dimensional (1D) band crossing in their electronic band structure, have been predicted to be potential catalysts in electrocatalytic processes. However, the current studies are limited to the TNLSMs where the dispersion around the nodal line is linear in all directions. Here, the potential application of the quadratic nodal line (QNL) semimetal Na₂CdSn in hydrogen evolution reaction is explored. Based on the bulk-boundary correspondence, we find that the topological surface states (TSSs) of the QNL are extended in the entire Brillouin zone. A linear relationship between the density of states of the TSSs and the Gibbs free energy is established in Na₂CdSn. Remarkably, the best performance of Na₂CdSn can be comparable to that of the noble metal Pt. Therefore, our work not only identifies an innovative type of topological catalyst with a QNL state but also confirms the relationship between TSSs and catalytic performance.

Keywords: Physics; Quantum physics.

Graphical abstract

Figure 1

Crystal structure and electronic structures (A) Crystal structure for Na₂CdSn. (B) Brillouin zone (BZ) of Na₂CdSn and the corresponding surface projection along the (100) and (010) directions. (C and D) Electronic band structures for Na₂CdSn without/with considering SOC, alongside with the corresponding density of states (DOS). The inset in (C) shows the dispersion relationship of nodal line along Γ-A path.

Figure 2

Topological surface states and energy slices (A, C, E, and G) Projected spectrum on the (010) and (100) surfaces without/with SOC in Na₂CdSn, where the arrows represent the drumhead and Fermi arc surface states of the quadratic nodal line and Dirac point. (B, D, F, and H) The slices under different energy values (−0.4 to 0.4 eV).

Figure 3

HER performance of different surfaces (A) Gibbs free energy of (100), (010), (111), (210), and (310) surfaces for Na₂CdSn and metal Pt. (B) Surface DOS values of (100), (010), (111), (210), and (310) surfaces for Na₂CdSn. (C) Linear relationship between surface DOS values and Gibbs free energy of (100), (010), (111), (210), and (310) surfaces. (D) Volcano map of Na₂CdSn, pure metals (Pt, Pb, Ag, and Cu) and some other topological materials (TaAs family, PtGa, and CoS₂).

Figure 4

Tuning the QNL and HER performance by electrons and holes doping (A) Schematic diagram of electrons/holes doping into Na₂CdSn lattice. (B) Changes of QNL positions, surface DOS values, and Gibbs free energy, when electrons and holes are doped into Na₂CdSn lattice. (C) Projection spectrum on the (010) surface of Na₂CdSn doped with 0.5 hole. (D) Gibbs free energy of Na₂CdSn by doping 0 and 0.5 holes.

Figure 5

Tuning the QNL and HER performance by moving atoms (A) Schematic diagram by moving Cd atoms in Na₂CdSn. (B) Electronic band structure after moving Cd atoms. The inset shows the dispersion relationship by breaking QNL. (C) Projected spectrum on the (010) surface by breaking QNL. (D) Changes of surface DOS values before and after breaking QNL. The inset shows the change of Gibbs free energy before and after breaking QNL.

Figure 6

Overpotential and charge density difference (A and B) The overpotential on the (010) and (100) surfaces, respectively. (C and D) Charge density difference on the (010) and (100) surfaces, respectively.