Spin Hall effect and topological surface states in a cubic Laves phase superconductor

In this work, we investigate the electronic structures, spin Hall effects, and topological properties of the superconductor ${\mathrm{YIr}}_{2}$, which crystallizes in the cubic Laves phase and contains two-dimensional (2D) kagome-lattice planes. We find it has an intrinsic 3D flat band originated from two intersecting kagome-lattice planes. This 3D flat band gives rise to large intrinsic spin Hall conductivity, which suggests ${\mathrm{YIr}}_{2}$ can be used for charge-spin conversion devices. On the (111) surface, it has Dirac-cone type topological surface states in close vicinity of the Fermi level. More importantly, they are distinct from the bulk states, indicating that ${\mathrm{YIr}}_{2}$ is a promising candidate topological superconductor to host Majorana zero modes. Our work provides an encouraging platform on which to study flat band physics, spin Hall effects, and topological superconductivity.