  Topological nodal-line semimetals are characterized by one-dimensional lines
of band crossing in the Brillouin zone. In contrast to nodal points, nodal
lines can be in topologically nontrivial configurations. In this paper, we
study the simplest topologically nontrivial forms of nodal line, namely, a
single nodal line taking the shape of a knot in the Brillouin zone. We
introduce a generic construction for various "nodal-knot semimetals", which
yields the simplest trefoil nodal knot and other more complicated nodal knots
in the Brillouin zone. The knotted-unknotted transitions by nodal-line
reconnections are also studied. Our work brings the knot theory to the subject
of topological semimetals.
