Specific heat of ⁴He confined in channels of 1 μm square cross-section

We report measurements of the specific heat near the superfluid transition of ⁴He confined in uniform channels of 1 μm square cross-section. This system undergoes a crossover from three dimensional behavior (3D) to 1D as the transition is approached. This results in a substantial rounding of the specific heat maximum as well as a shift to colder temperatures relative to the bulk system. We compare these data to previous measurements where crossovers from 3D to 2D and 0D were studied with the smallest confining dimension being the same (1 μm) in each case. We also compare these results in the context of finite-size scaling to previous studies where crossover to 1D was measured in cylindrical geometries. We identify regions where surface and edge effects dominate the specific heat, and compare these amplitudes to theory, where available. The realization of the confining geometry in this work is achieved with a combination of silicon lithography and direct wafer bonding.