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Valence and conduction bands in nodal loop semimetals (NLSMs) touch alongclosed loops in momentum space. If such loops can proliferate and linkintricately, NLSMs become exotic topological phases with unconventionaltopological characteristics and potentially peculiar transport properties. Inconventional quantum materials or cold atom systems alike, such exotic phasesnecessarily require non-local hopping and are therefore intrinsicallyunrealistic. In this work, we show how this hurdle can be surmounted through anexperimentally feasible periodic driving scheme. In particular, by tuning theperiod of a two-step periodic driving or some experimentally accessibleparameters, we show how to generate arbitrarily many nodal loops that arelinked with various levels of complexity. Furthermore, we propose to use boththe Berry phase winding and the Alexander polynomial topological invariant tocharacterize the fascinating linkages among the nodal loops. This work thuspresents a class of exotic Floquet topological phase that has hitherto not beenproposed in any realistic setup.

Realistic Floquet semimetal with exotic topological linkages between arbitrarily many nodal loops