Charged interface ofHe3-He4mixtures. Softening of interfacial waves

The excitation spectrum of ripplons at the charged interface of phase-separated ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures has been determined for electric fields $E$ up to $E_c$, given by the stability limit of the interface. The frequency $\frac{\omega }{2\pi }$ of the ripplons is substantially reduced by the presence of the charges, most pronounced for excitations with a wave vector $q_c$ equal to the inverse capillary length, where $\omega \to 0$ when the electric field approaches the critical value $E_c$. Both $E_c$ and $q_c$ depend on temperature via the interfacial properties. In the investigated temperature region, $0.5<T<\mathrm{}0.77\mathrm{}$ K, and for two types of charge carriers, negative and positive ions, the experimentally determined ripplon softening is well accounted for by the theory.