  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.
