Optical bounds on many-electron localization

TL;DR

This paper derives rigorous optical bounds relating insulator properties like electron localization, susceptibility, and gap, providing practical estimates of localization length from experimental data and revealing connections to van der Waals physics.

Contribution

It introduces new inequalities linking optical properties and electron localization, with bounds applicable to experimental data and analytical models.

Findings

Bounds on localization length can be estimated from experimental data.

Localization lengths follow chemical trends, especially in alkali halides.

Analytical models connect optical bounds to van der Waals forces.

Abstract

We establish rigorous inequalities between different electronic properties linked to optical sum rules, and organize them into weak and strong bounds on three characteristic properties of insulators: electron localization length $\ell$ (the quantum fluctuations in polarization), electric susceptibility $\chi$, and optical gap $E_{\rm G}$. All-electron and valence-only versions of the bounds are given, and the latter are found to be more informative. The bounds on $\ell$ are particularly interesting, as they provide reasonably tight estimates for an ellusive ground-state property - the average localization length of valence electrons - from tabulated experimental data: electron density, high-frequency dielectric constant, and optical gap. The localization lengths estimated in this way for several materials follow simple chemical trends, especially for the alkali halides. We also illustrate our findings via analytically solvable harmonic oscillator models, which reveal an intriguing connection to the physics of long-ranged van der Waals forces.