Topological spin corner charge in the presence of spin-orbit coupling

We investigate several $C_6$ second order topological insulators that are independently topological or trivial for two different spins, or pseudo-spins, using tight binding models and first principles electromagnetic simulations in the presence of spin orbit coupling (SOC). When the insulator is second order topological for both spins the corner charge is quantized to 0 and a topological phase transition can occur due to SOC. However, when the insulator is second order topological for only one of the spins, the corner charge is quantized to 1/2 and no topological transition can manifest.