Effects of spin-orbit coupling in a valley chiral kagom\'e network

Valley chiral kagom\'e networks can arise in various situations, like for example, in double-aligned graphene-hexagonal boron nitride and periodically strained graphene. Here, we construct a phenomenological scattering model based on the symmetries of the network to investigate the energy spectrum and magnetotransport in this system. Additionally, we consider the effects of a finite Rashba spin-orbit coupling on the transport properties of the kagom\'e network. We identify conditions where the interplay of the Rashba spin-orbit coupling and the geometry of the lattice results in a reduction of the periodicity of the magnetoconductance and characteristic sharp resonances. Moreover, we find a finite spin-polarization of the conductance, which could be exploited in spintronic devices.