  Valence and conduction bands in nodal loop semimetals (NLSMs) touch along
closed loops in momentum space. If such loops can proliferate and link
intricately, NLSMs become exotic topological phases with unconventional
topological characteristics and potentially peculiar transport properties. In
conventional quantum materials or cold atom systems alike, such exotic phases
necessarily require non-local hopping and are therefore intrinsically
unrealistic. In this work, we show how this hurdle can be surmounted through an
experimentally feasible periodic driving scheme. In particular, by tuning the
period of a two-step periodic driving or some experimentally accessible
parameters, we show how to generate arbitrarily many nodal loops that are
linked with various levels of complexity. Furthermore, we propose to use both
the Berry phase winding and the Alexander polynomial topological invariant to
characterize the fascinating linkages among the nodal loops. This work thus
presents a class of exotic Floquet topological phase that has hitherto not been
proposed in any realistic setup.
