Three-Dimensional Critical Behavior with 2D, 1D, and 0D Dimensionality Crossover: Surface and Edge Specific Heats

The specific heat of helium confined at the smallest dimension but with different dimensionality crossover was investigated. The surface and line specific heat contributions were identified by analyzing the deviation of the specific heat from its behavior in the thermodynamic limit. By a combination of silicon lithography and direct wafer bonding, the design of the cells was made possible. It was observed that the ordered state of liquid helium is characterized by a macroscopic wave function, which is often assumed to obey Dirichlet boundary conditions at walls.