The electronic structure of materials: from high-throughput explorations to novel foundations.

The electronic structure of materials encodes their electronic, optical, magnetic and topological properties, and it is often discussed in terms of Bloch orbitals and band structures. Wannier functions provide an alternative, chemically intuitive representation; in particular, maximally localized Wannier functions - introduced close to 30 years ago - are widely used nowadays to calculate accurately and efficiently many properties of interest, from electron mobilities to BCS superconducting temperatures. Here, we first showcase two key algorithms that we recently developed (projectability disentanglement and manifold remixing) that allow to fully automate the calculation of Wannier functions that represent the most compact and most precise Hamiltonian describing the occupied and lowest unoccupied bands, and that can be mixed into desired target manifolds (e.g., the valence bands of insulators, or selected correlated bands). Starting from our MC3D database of experimentally known stoichiometric inorganics (https://mc3d.materialscloud.org), we construct ~2M Wannier functions for 21,737 materials and for a subset of 5032 that are band semiconductors or insulators. This allows us to identify high-performance thermoelectrics, discover candidate materials with large non-linear Hall response, and design heterostructures that support a two-dimensional electron gas at the interface. While these explorations are based on Kohn-Sham density-functional theory, I will highlight the next foundational step that delivers spectral functionals and spectral theories. Namely, I’ll discuss orbital-density-dependent functionals that describe the correct band structure and band gap, and functionals dependent on the spectral density that can also describe satellites and correlated-electron materials.