  Topological nodal line semimetals are characterized by the crossing of the
conduction and valence bands along one or more closed loops in the Brillouin
zone. Usually, these loops are either isolated or touch each other at some
highly symmetric points. Here, we introduce a new kind of nodal line semimetal,
that contains a pair of linked nodal loops. A concrete two-band model was
constructed, which supports a pair of nodal lines with a double-helix
structure, which can be further twisted into a Hopf link because of the
periodicity of the Brillouin zone. The nodal lines are stabilized by the
combined spatial inversion $\mathcal{P}$ and time reversal $\mathcal{T}$
symmetry; the individual $\mathcal{P}$ and $\mathcal{T}$ symmetries must be
broken. The band exhibits nontrivial topology that each nodal loop carries a
$\pi$ Berry flux. Surface flat bands emerge at the open boundary and are
exactly encircled by the projection of the nodal lines on the surface Brillouin
zone. The experimental implementation of our model using cold atoms in optical
lattices is discussed.
