  Superconducting and topological states are two quantum phenomena attracting
much interest. Their coexistence may lead to topological superconductivity
sought-after for Majorana-based quantum computing. However, there is no causal
relationship between the two, since superconductivity is a many-body effect due
to electron-electron interaction while topology is a single-particle
manifestation of electron band structure. Here, we demonstrate a novel form of
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing, induced by topological Weyl
nodal lines in Ising Bardeen-Cooper-Schrieffer (IBCS) superconductors. Based on
first-principles calculations and analyses, we predict that the nonmagnetic
metals of MA$_2$Z$_4$ family, including ${\alpha}_1$-TaSi$_2$P$_4$,
${\alpha}_1$-TaSi$_2$N$_4$, ${\alpha}_1$-NbSi$_2$P$_4$,
${\alpha}_2$-TaGe$_2$P$_4$, and ${\alpha}_2$-NbGe$_2$P$_4$ monolayers, are all
superconductors. While the intrinsic IBCS paring arises in these
non-centrosymmetric systems, the extrinsic FFLO pairing is revealed to be
evoked by the Weyl nodal lines under magnetic field, facilitating the formation
of Cooper pairs with nonzero momentum in their vicinity. Moreover, we show that
the IBCS pairing alone will enhance the in-plane critical field $B_c$ to ~10-50
times of Pauli paramagnetic limit $B_p$, and additional FFLO pairing can
further triple the $B_c/B_p$ ratio. It therefore affords an effective approach
to enhance the robustness of superconductivity. Also, the topology induced
superconductivity renders naturally the possible existence of topological
superconducting state.
