Spin splitting and spin Hall conductivity in buckled monolayers of group 14: First-principles calculations

Elemental monolayers of the group 14 with a buckled honeycomb structure, namely silicene, germanene, stanene, and plumbene, are known to demonstrate spin splitting as result an electric field parallel their high symmetry axis which is capable tuning topological phase between quantum Hall insulator ordinary band insulator. We perform first-principles calculations based on density functional theory quantify spin-dependent gaps function applied extract main coefficients invariant Hamiltonian. Using linear response Wannier interpolation method, we calculate conductivity in study its sensitivity external field. Our results show that not quantized case stanene degrades significantly inverts gap brings monolayer into trivial phase. The induced does close plumbene shows robust