Weyl Points Enabled by Three-dimensional Flat Band*

Topological flat band (FB) has attracted much interest because it exhibits a range of exotic quantum phases. Here, we discover yet another novel physical manifestation arising from three-dimensional (3D) FB but absent for 2D FB. We show that in the presence of spin-orbit coupling, magnetization of 3D FBs induces a transition from a 3D topological insulator (TI) into a Weyl semimetal, while for a 2D FB a transition from a 2D TI into a Chern insulator is known previously. The Weyl semimetal so formed may contain only a minimum of two Weyl points. The formation of Weyl points by symmetry breaking of highly degenerate 3D FBs is distinctively different from the conventional mechanism by symmetry breaking of a Dirac point. We demonstrate this unusual 3D-FB-enabled Weyl state first in a pyrochlore lattice model using tight-binding method and then in a real material Sn₂Nb₂O₇ using first-principles calculations. The main features of the resulting Weyl points are analyzed with respect to symmetry, topological invariant and surface state. The Weyl fermions associated with FB may open new frontiers in the research of topological physics and materials.