Faraday Instability of Crystallization Waves at theHe4Solid-Liquid Interface

Crystallization waves exist at the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ solid-liquid interface at low temperatures that are analogous to capillary waves at a liquid-air interface. Standing capillary waves can also be excited parametrically leading to the so-called Faraday instability. We analyze here the analog of this instability for crystallization waves. The threshold for the instability is independent of the surface stiffness at low temperatures, and therefore also independent of the crystalline anisotropy. The symmetry of surface patterns above the instability threshold, on the other hand, is argued to be sensitive to crystalline anisotropy.