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The interplay between symmetry and topology led to the concept ofsymmetry-protected topological states, including all non-interacting and weaklyinteracting topological quantum states. Among them, recently proposed nodalline semimetal states with space-time inversion ($\mathcal{PT}$) symmetry whichare classified by the Stiefel-Whitney characteristic class associated with realvector bundles and can carry a nontrivial $\mathbb{Z}_2$ monopole charge haveattracted widespread attention. However, we know less about such 3D$\mathbb{Z}_2$ nodal line semimetals and do not know how to construct them. Inthis work, we first extend the layer construction previously used to constructtopological insulating states to topological semimetallic systems. We construct3D $\mathbb{Z}_2$ nodal line semimetals by stacking of 2D$\mathcal{PT}$-symmetric Dirac semimetals via nonsymmorphic symmetries. Basedon our construction scheme, effective model and combined with first-principlescalculations, we predict two types of candidate electronic materials for$\mathbb{Z}_2$ nodal line semimetals, namely 14 Si and Ge structures and 108transition metal dichalcogenides $MX_2$ ($M$=Cr, Mo, W, $X$=S, Se, Te). Ourtheoretical construction scheme can be directly applied to metamaterials andcircuit systems. Our work not only greatly enriches the candidate materials anddeepens the understanding of $\mathbb{Z}_2$ nodal line semimetal states butalso significantly extends the application scope of layer construction.

Layer Construction of Three-Dimensional Z2 Monopole Charge Nodal Line Semimetals and prediction of the abundant candidate materials