Multiorbital Flat Band Ferromagnetism with a Provable Percolation Representation*

We consider a two-layer multiorbital system consisting of a p_x- and p_y-orbital honeycomb lattice layer and an f_y(3x²-y²)-orbital triangular lattice layer centered on the honeycomb plaquettes. With an appropriately tuned chemical potential difference between these two layers, the system exhibits a flat band with provably ferromagnetic ground states at half filling in the presence of intra-orbital Hubbard interactions and Hund’s coupling. Away from half filling, the interacting system admits a percolation representation, where the ground state space is spanned by maximum-spin clusters of localized single-particle states. A paramagnetic-ferromagnetic transition occurs as the band approaches half filling and the space of degenerate ground states becomes dominated by clusters with macroscopic spin. The critical filling of the flat band where this transition occurs can be found through Monte Carlo simulation for spin-weighted percolation.