Deep connection between metallicity and symmetry

What is it about?

We reveal a deep connection of the presence of the insulating gap with the structure and symmetry of the solid. The connection is through the optical phonons. On the one hand, these underlie the lattice polarization, which must also occur during electronic excitations across the gap. On the other hand, the optical phonons are present only when the primitive cell of the crystal has at least two atoms. As a result, solids that are so symmetric as to have only one atom per primitive cell must be metallic, with the exception of exotic systems such as noble elements or ferromagnetic Wigner crystals. The present approach naturally yields a connection between the vibrational and electronic properties of the solid.

Featured Image

Why is it important?

In addition to providing a qualitative explanation of an important phenomenon, this work explicitly describes the metal-insulator transition as a symmetry lowering of the electronic fluid. This has the potential to tap into successful quantitative methodologies developed earlier for classical fluids, but not until quantum effects are properly included. The "quantumness" reveals itself in the order parameter for the transition being two-component; the components reflect the amount of electronic fluid at lattice sites and interatomic space, respectively. (Just one component would suffice for classical fluids.) Because the order parameter is two-component, the symmetry breaking underlying the transition is continuous; still, the transition does not cause the emergence of Goldstone modes, which we show explicitly.

Perspectives