Role of the third dimension in searching for Majorana fermions in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mtext>−</mml:mtext><mml:msub><mml:mi>RuCl</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> via phonons
Sai Mu, Kiranmayi D. Dixit, Xiaoping Wang, D. L. Abernathy, Huibo Cao, S. E. Nagler, Jiaqiang Yan, Paula Lampen-Kelley, David Mandrus, Carlos A. Polanco, Liangbo Liang, Gábor B. Halász, Yongqiang Cheng, Arnab Banerjee, Tom Berlijn
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.