Barry Bradlyn

Abstract We introduce stable real-space invariants (SRSIs), topological invariants defined from adiabatic deformations between Wannier states, generalizing previously discovered local and composite real-space invariants. SRSIs are \({\mathbb{Z}}\)- and \({{\mathbb{Z}}}_{n}\)-valued (n = 2, 4) linear combinations of Wannier state multiplicities characterizing the stable equivalence of atomic insulators. We enumerate all SRSIs in nonmagnetic space groups with and without spin-orbit coupling.

Using inelastic x-ray scattering (IXS), we experimentally investigate the quantum geometry and quantum information in the large-gap insulator, LiF. Using sum rules for the density-density response function measured in IXS, we compute the quantum Fisher information of the equilibrium density matrix of LiF associated with density perturbations.

We examine the hydrostatic stress of electrons strongly confined in a quasi-two-dimensional quantum well in the presence of a strong perpendicular and weak in-plane magnetic field. This introduces anisotropy into the stress tensor which is inconsistent with the notion of the quantum Hall droplet as a simple two-dimensional electron fluid.