Phonon Quantum Phase Transition

We show that a quantum phase transition can occur in a phonon system in the presence of dislocations. Due to the competing nature between the topological protection of the dislocation and anharmonicity, phonons can reach a quantum critical point at a frequency determined by dislocation density and the anharmonic constant, at zero temperature. In the symmetry-broken phase, a novel phonon state is developed with a dynamically-induced dipole field. We carry out a renormalization group analysis and show that the phonon critical behavior differs wildly from any electronic system. In particular, at the critical point, a single phonon mode dominates the density of states and develops an exotic logarithmic divergence in thermal conductivity. This phonon quantum criticality provides a completely new avenue to tailor phonon transport at the single-mode level without using phononic crystals.