Quantum geometric bounds in ionic and covalent insulators measured with inelastic x-ray scattering

Widespread interest in topological phases of matter has recently raised awareness of the importance of quantum geometry in solids. The topology of an electronic energy band is quantified by its Berry curvature, which is the imaginary part of a more general quantity called the quantum geometric tensor, Tmn. Its real part, the quantum metric, characterizes electronic polarization fluctuations and is a measure of the delocalization of valence electrons in a material. These fluctuations can be expressed in terms of the quantum weight, K(q), which is proportional to the quantum Fisher information, a measure of the number of entangled degrees of freedom per unit volume in a quantum system. These relationships imply a deep connection between quantum geometry, entanglement, and the nature of chemical bonding in solids. 

In this talk, I will present an experimental investigation of these ideas using inelastic x-ray scattering (IXS) from two prototypical insulators, covalently bonded diamond and ionically bonded LiF. Extracting the quantum weight from the IXS data demonstrates that, in diamond, the delocalization of electronic information extends over multiple unit cells, while in LiF it is confined within a single unit cell. In both cases, the quantum weight lies within fundamental bounds recently postulated for insulating states of matter [1,2]. Our results align with the intuitive understanding of covalent and ionic bonding, and demonstrate that energy-loss scattering provides a quantitative probe of wave function geometry in solids.

[1] Y. Onishi, L. Fu, PRX 14, 011052 (2024)

[2] D. Balut, M. D. Collins, B. Bradlyn, P. Abbamonte, arXiv:2601.19054