Flat Bands Arising from Spin-Orbit Assisted Orbital Frustration

We present general design principles for engineering and discovering periodic systems with flat bands. Our paradigm exploits spin-orbit assisted orbital frustration on a lattice to produce band structures that contain multiplets of narrowly dispersing bands whose bandwidth is smaller than all other energy scales of the problem including the band gap surrounding the flat bands. We present a series of models in 1D and 2D on various lattices with different intracellular spin-orbit like potentials that hybridize the degrees of freedom in the unit cell. As an alternative to machine learning based exhaustive searches, these design principles and models can be used to search for flat band systems in a variety of physical settings and can be used to investigate the role of weakly dispersing highly orbitally frustrated degrees of freedom in systems where the interactions dominate over the kinetic energy scales of the system.