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An isotropic tight-binding model with the nearest-neighbour hopping on a pyrochlore lattice gives a rich variety of physical properties due to the emergence of the flat-band. Moreover, by introducing spin-orbit coupling into this model, the topological properties of the system changes significantly. This model is well applicable to some pyrochlore oxides called s1/s2 pyrochlores. In this paper we apply this model to an s2 pyrochlore oxide Pb 2 Ta 2 O 7  and found a characteristic quadratic touching of the quasi-flat band and dispersive band. Furthermore, when a ferromagnetic order appears due to this quasi-flat band, a pair of Weyl points appears in that direction.

Quasi-Flat-Band in s1/s2 Pyrochlore Oxides and the Effect of Spin-Orbit Interaction