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We study within the framework of the Lifshitz theory the long-range Casimirforce for in-plane isotropic and anisotropic free-standing transdimensionalmaterial slabs. In the former case, we show that the confinement-inducednonlocality not only weakens the attraction of ultrathin slabs but also changesthe distance dependence of the material-dependent correction to the Casimirforce to go as $\sim\!1/\!\sqrt{l}$ contrary to the $\sim\!1/l$ dependence ofthat of the local Lifshitz force. In the latter case, we use closely packedarray of parallel aligned single-wall carbon nanotubes in a dielectric layer offinite thickness to demonstrate strong orientational anisotropy and crossoverbehavior for the inter-slab attractive force in addition to its reduction withdecreasing slab thickness. We give physical insight as to why such a pair ofultrathin slabs prefers to stick together in the perpendicularly orientedmanner, rather than in the parallel relative orientation as one wouldcustomarily expect.

Confinement-Induced Nonlocality and Casimir Force in Transdimensional Systems