Topological Fermi Liquids in Multi-band Systems

Monopole superconducting and density-wave orders have been proposed in topological semimetal systems when pairing occurs between Fermi surfaces with different Chern numbers. The resulting orders are distinguished from the familiar s-, p-, and d-wave pairing orders by a nonzero pair monopole charge and are described by monopole harmonics. We generalize the framework above to explore topological Fermi liquids in multi-band systems with topological Fermi surfaces and inter-band interactions. We investigate the monopole harmonic generalization of sound modes in higher partial wave channels and exotic collective modes.