Two-dimensional potassium borides with hidden kagome-like lattice: Topological semimetals, van Hove singularities, and superconductivity

The coexistence of nontrivial topological properties and superconductivity in a material offers the potential to achieve topological superconductivity and Majorana zero modes. However, research on ideal topological semimetals with superconductivity has been limited. In this paper, we utilize first-principles calculations to predict the existence of three two-dimensional potassium borides (${\mathrm{K}}_{2}{\mathrm{B}}_{9}, {\mathrm{KB}}_{9}$, and ${\mathrm{KB}}_{18}$) with a hidden kagome-like lattice structure, inspired by the arrangement of the ${\mathrm{K}}_{2}{\mathrm{B}}_{9}{}^{\ensuremath{-}}$ cluster in an inverse sandwich configuration. Our findings reveal that all three materials exhibit phonon-mediated superconductivity, with transition temperatures (${T}_{c}$) of 12.56, 14.46, and 10.50 K, respectively. Furthermore, ${\mathrm{K}}_{2}{\mathrm{B}}_{9}$ and ${\mathrm{KB}}_{18}$ are identified as topological nodal-line semimetals, while ${\mathrm{KB}}_{9}$ demonstrates the characteristics of an ideal Dirac semimetal due to the broken ${\ensuremath{\sigma}}_{h}$ mirror symmetry and appropriate potassium content. The topological properties arise from the band inversion of the boron atom's $p{}_{x}+p{}_{y}$ and $p{}_{z}$ orbitals within the ${\mathrm{B}}_{9}$ layer. Intriguingly, ${\mathrm{KB}}_{9}$ exhibits coexisting Dirac points and van Hove singularities near the Fermi level, which are a consequence of the hidden kagome-like lattice, thereby enhancing the superconducting transition temperature (${T}_{c}$). This research not only sheds light on the pivotal role played by the orbital character of the ${\mathrm{B}}_{9}$ layer in the kagome-like lattice of potassium borides but also presents a strategy for achieving the coexistence of topological properties and superconductivity, thereby opening up possibilities for the realization of exotic physics.