Role of the third dimension in searching for Majorana fermions in α−RuCl3 via phonons

Abstract

Understanding phonons in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ is critical to analyze the controversy around the observation of the half-integer thermal quantum Hall effect. While many studies have focused on the magnetic excitations in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, its vibrational excitation spectrum has remained relatively unexplored. We investigate the phonon structure of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ via inelastic neutron-scattering experiments and density-functional-theory calculations. Our results show excellent agreement between experiment and first-principles calculations. After validating our theoretical model, we extrapolate the low-energy phonon properties. We find that the phonons in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ that either propagate or vibrate in the out-of-plane direction have significantly reduced velocities and therefore have the potential to dominate the observability of the elusive half-integer plateaus in the thermal Hall conductance. In addition, we use low-energy interlayer phonons to resolve the low-temperature stacking structure of our large crystal of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, which we find to be consistent with that of the $R\overline{3}$ space group, in agreement with neutron diffraction.