Discovery and Prediction on a Family of Hard Superconductors with Kagome Lattice: <i>XY</i>₃ 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 NaSi₃_<i>P</i>6/<i>mmm</i> phase of Na_<i>x</i>Si_<i>y</i> (<i>x</i>, <i>y</i> = 1-3). For a comprehensive understanding of <i>XY</i>₃_<i>P</i>6/<i>mmm</i>, other atoms such as <i>X</i> = Li, Na, Cs and <i>Y</i> = B, Si, Ge are included. Superconducting critical temperatures (<i>T</i>_c) of <i>XY</i>₃ compounds are calculated between 0 and 20 GPa and found to be 30.54 K for CsB₃ at 0 GPa, indicating that electron-phonon coupling, phonon softening, linewidths, and electron density at the Fermi level all have significant effects on <i>T</i>_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 NaSi₃_<i>P</i>6/<i>mmm</i> is determined to be 608 K at 0 GPa and <i>P</i>-<i>T</i> phase diagram at pressures of 0-15 GPa using deep learning molecular dynamics simulations. Our findings provide a multitude of excellent properties in the <i>XY</i>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.