title: Quantum Critical Elasticity.
abstract: We discuss elastic instabilities of the atomic crystal lattice at zero temperature. Because of long-range shear forces of the solid, at such transitions the phonon velocities vanish, if at all, only along certain crystallographic directions, and, consequently, the critical phonon fluctuations are suppressed to a lower dimensional manifold and governed by a Gaussian fixed point. In the case of symmetry-breaking elastic transitions, a characteristic critical phonon thermodynamics arises that is found, e.g., to violate Debye's T(3) law for the specific heat. We point out that quantum critical elasticity is triggered whenever a critical soft mode couples linearly to the strain tensor. In particular, this is relevant for the electronic Ising-nematic quantum phase transition in a tetragonal crystal as discussed in the context of certain cuprates, ruthenates, and iron-based superconductors.
authors.affiliation: Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany.
authors.forename: Mario
authors.initials: M
authors.lastname: Zacharias
authors.affiliation: Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot-Paris 7 & CNRS, UMR 7162, 75205 Paris, France.
authors.forename: Indranil
authors.initials: I
authors.lastname: Paul
authors.affiliation: Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany.
authors.forename: Markus
authors.initials: M
authors.lastname: Garst