We introduce ''Berry-dipole semimetals'', whose band degeneracies are characterized by quantized Berry dipoles. Through a two-band model constructed by Hopf map, we reveal that the Berry-dipole semimetals display a multitude of salient properties distinct from other topological semimetals. On the boundary, we find that the first-order Berry-dipole semimetal harbors anomalous paired Fermi arcs with the same spin polarization, even though the layer Chern number is zero, and the second-order Berry-dipole semimetal hosts dispersionless hinge arcs. In the bulk, we find that the low-energy Berry-dipole Hamiltonian near the band node has a quadratic energy dispersion and peculiar Berry curvature, which give rise to rather unique characteristics in the intrinsic anomalous Hall effect, orbital magnetization and Landau levels. Our study shows that Berry-dipole semimetals are a class of topological gapless phases supporting rich intriguing physics.

7+12 pages, 7 figures