Electronic phases in pyrochlore flat band*

The past decade has witnessed enormous success in the fabrication and characterization of flat-band materials. Among various system platforms, there is one family where the flat bands are inherent in the lattice due to frustrated hoppings. In this talk, I show that the pyrochlore lattice, a member of this family, offers a fertile ground for novel correlated phases in the flat bands. With the Hartree-Fock approximation, I present, for the first time, the rich mean-field phase diagram of repulsive Hubbard model across all flat band filling. In addition to the flat-band ferromagnetism, our analysis yields cascades of unconventional magnetic orders as filling changes. These include a series of antiferromagnetic (AFM) spin-charge layer orders, as well as an evolution of noncoplanar spin orders with tetrahedral structures. I further benchmark our Hartree-Fock results by a symmetry analysis of regular magnetic orders on the pristine and breathing pyrochlore lattices. Our study sheds light on the search for novel magnetic orders in the pyrochlore flat-band materials, including CeRu2 and related compounds.