Quantum Fingering of the Inverted Liquid-Crystal ⁴He Interface in the Field of Gravity

Abstract

The simplest example of fingering occurs when a heavier liquid occupies the half-space above a lighter one. The fingers of the heavier liquid driven by gravity grow down, displacing the lighter liquid upward. The fingering of the superfluid phase into the ⁴He crystal facet below its roughening transition temperature can provide us an example of macroscopic quantum nucleation phenomena. Due to cusp-like singularity in the surface tension as a function of the facet orientation the crystal facet has a relative stability and its fingering is accompanied by overcoming some critical nucleation barrier. The barrier height is proportional to the square of the facet step energy and depends on a ratio of the facet size to the capillary length. At sufficiently low temperatures the thermal activation mechanism for the interface fingering is replaced with the quantum one associated with the penetration through the nucleation barrier.