Quantum critical elasticity

TL;DR

This paper explores quantum critical elasticity, where elastic instabilities at zero temperature lead to unique phonon behaviors and thermodynamics, especially relevant for electronic nematic transitions in high-temperature superconductors.

Contribution

It introduces the concept of quantum critical elasticity, analyzing how long-range shear forces and directional phonon velocity vanishing influence critical phenomena.

Findings

Critical phonon fluctuations are suppressed to lower-dimensional manifolds.

Elastic transitions can violate Debye's T^3 specific heat law.

Quantum critical elasticity is linked to soft modes coupling linearly to strain.

Abstract

We discuss elastic instabilities of the atomic crystal lattice at zero temperature. Due to 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 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.