Metal-Insulator Transitions in Elastic Media
Abstract: The metal-insulator transition driven by strong electronic correlations — generically called the "Mott" transition — is usually described entirely by electronic Hamiltonians, with models designed to exhibit related emergent phenomena such as magnetism and superconductivity. In real solids, the electronic localization also couples to the crystal lattice, and it turns out that these elastic degrees of freedom insert important new entropic phenomena more familiar in soft matter physics.
The coupling to the lattice induces elastic strain fields, which have intrinsic long-range interactions that cannot be screened. When strain fields are produced as a secondary order parameter in phase transitions — as for example in ferroelectrics — this produces unexpected consequences for the dynamics of order parameter fluctuations, including the generation of a gap in what would otherwise have been expected to be Goldstone modes.
A very important class of transition metal oxides — the perovskites – can be thought of as an array of tethered octahedra where the Mott transition produces a shape-change in the unit cell. Coupling of the fundamental order parameter to octahedral rotations gives rise to large entropic effects that can shift the transition temperature by hundreds of degrees Kelvin, essentially by exploiting the physics of jammed solids. The insight might offer ways to make better refrigerators by enhancing electro-caloric and magneto-electric effects.