Collective lattice excitations in the dynamic route for melting hydrodynamic two-dimensional crystals

Abstract

Liquid surface stiffness generates stable Faraday wave (FW) patterns, known as hydrodynamic crystals, which form resonant FW lattices composed of discrete harmonics and subharmonics under monochromatic driving. Key interactions include inertia-driven parametric resonance, which halves subharmonic modes, and surface rigidity harnessing three-wave coupling, which focuses the nonlinear harmonic wave field. Here, we reveal these wave interaction processes allowing coherent FW packets to organize in space and time while also exciting decoherent disorder in the hydrodynamic crystal lattice. Collective excitations are shown to emerge as dispersionless dislocation waves, causing periodic amplitude modulations due to explicit symmetry breaking. From a field theory perspective, we show chaotic FW degeneration leading to hydrodynamic crystal melting via continuous mode halving under forcing, akin to Landau's theory of chaotic turbulence.