We study the distinctive features of the interplay between the interlayer superconductivity and ferroelectricity in van der Waals heterostructures. Corresponding analysis is carried out within the framework of the quasiclassical Eilenberger equations for a tunnel coupled bilayer with inhomogeneous relative shift of the conduction bands between the layers, which describes the net charge transfer in sliding ferroelectrics. It is shown that the critical temperature of the interlayer superconductivity can be significantly enhanced for superconducting nuclei localized in the vicinity of ferroelectric domain walls. We demonstrate that the increase in the tunneling amplitude leads to the decrease (increase) in the difference between the critical temperatures for localized and homogeneous superconducting states for the spin-singlet (spin-triplet) interlayer superconductivity. We also perform an extensive analysis of the effects of the in-plane magnetic field on the interlayer superconductivity. It is shown that the orbital effect can result in the suppression of the spin-singlet interlayer superconductivity and to the enhancement of the spin-triplet one. We find that possible manifestations of the paramagnetic effect include the suppression of the interlayer superconductivity by rather weak Zeeman fields, the two-fold anisotropy of the critical magnetic field for the spin-triplet states, as well as the appearance of reentrant superconducting phases. It is shown that the joint influence of the orbital and paramagnetic mechanisms on the spin-triplet interlayer superconductivity can even lead to a nonmonotonic behavior of the superconducting critical temperature as a function of the external magnetic field. The results are discussed in the context of recent experimental data on van der Waals structures with coexisting superconductivity and sliding ferroelectricity.

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• Ferroelectric domains
• Ferroelectricity
• Superconducting phase transition
• Superconductivity
• Transition temperature
• van der Waals systems
• Green's function methods