Kane-Lubensky phonons in Maxwell lattice frustrated Mott insulators

RESUMO

We show that zero-energy gapless Weyl-line phonons of the Kane-Lubensky's type can arise in the three-dimensional Maxwell lattice frustrated Mott insulators through the magnetopological mechanics. In a pyrochlore antiferromagnet with the spin-lattice coupling, a magnetic field selects the spin state whose lattice distortion generates a $P4_3 32$ topological lattice. More crucially, the spin-lattice coupling and the spin configuration cause the bending of the neighbouring bonds, and converts the system into the topological Maxwell lattice. Remarkably, the resulting system is found to host the bulk zero-frequency Weyl-line phonons protected topologically, and these gapless phonons are not Goldstone modes. Unlike the conventional ${C_{\rm ph}\sim T^3}$ for the Goldstone phonons, these one-dimensional zero-mode manifolds yield a characteristic low-temperature phonon specific heat ${C_{\rm ph}\sim T^2}$. Our results could find applications in the Cr-based spinel systems, and moreover, we establish a low-energy platform where an extensive number of topological zero-frequency phonons can strongly couple to other degrees of freedom, opening a route to exotic phonon-mediated phenomena.