Discovery and Prediction on a Family of Hard Superconductors with Kagome Lattice: XY₃ Compounds

The search for and design of superconductors with both Kagome lattice and hardness is a challenging and frontier research topic. This work utilizes structure predictions to discover the Kagome lattice in NaSi 3 _ P 6/ mmm phase of Na x Si y ( x, y = 1–3). For a comprehensive understanding of XY 3 _ P 6/ mmm, other atoms such as X = Li, Na, Cs and Y = B, Si, Ge are included. Superconducting critical temperatures ( T c ) of XY 3 compounds are calculated between 0 and 20 GPa and found to be 30.54 K for CsB 3 at 0 GPa, indicating that electron–phonon coupling, phonon softening, linewidths, and electron density at the Fermi level all have significant effects on T c . The bonding type of B, Si, and Ge atoms in the Kagome lattice also determines the boundaries of its hard properties and superconductivity. Moreover, the melting temperature of NaSi 3 _ P 6/ mmm is determined to be 608 K at 0 GPa and P – T phase diagram at pressures of 0–15 GPa using deep learning molecular dynamics simulations. Our findings provide a multitude of excellent properties in the XY 3 compounds, including Kagome lattice, high hardness, and superconductors, which will provide essential physical insights and theoretical guidance for the experimental exploration of the hard superconductors.