⁴He confined to 1 μm³ boxes, 0D crossover, surface and edge effects

We report measurements of the specific heat near the superfluid transition of ⁴He confined to 1 μm³ cylindrical boxes patterned in SiO₂. This system crosses from a 3D behavior to a 0D behavior near the transition. This has a marked effect on the specific heat as seen by a pronounced rounding of the maximum and a shift to a temperature much lower than the transition of the bulk system (and systems with 2D or 1D crossover). We plot the data according to correlation-length scaling theory and compare this to a planar system with the same smallest confinement. Compared to our previous studies of planar systems, the 0D cell has 3 × the surface to volume ratio as well as ∼750 × as much edge length. We examine the regions where surface and edge effect contributions can be separated. We find that the data do not reach the expected value for the surface region. There is also evidence for a region where the term associated with edge contributions dominates.