Unconventional materials: the mismatch between electronic charge centers and atomic positions.

The complete band representations (BRs) have been constructed in the work of topological quantum chemistry. Each BR is expressed by either a localized orbital at a Wyckoff site in real space, or by a set of irreducible representations in momentum space. In this work, we define unconventional materials with a common feature of the mismatch between average electronic centers and atomic positions. They can be effectively diagnosed as whose occupied bands can be expressed as a sum of elementary BRs (eBRs), but not a sum of atomic-orbital-induced BRs (aBRs). The existence of an essential BR at an empty site is described by nonzero real-space invariants (RSIs). The "valence" states can be derived by the aBR decomposition, and unconventional materials are supposed to have an uncompensated total "valence" state. The high-throughput screening for unconventional materials has been performed through the first-principles calculations. We have discovered 423 unconventional compounds, including thermoelectronic materials, higher-order topological insulators, electrides, hydrogen storage materials, hydrogen evolution reaction electrocatalysts, electrodes, and superconductors. The diversity of these interesting properties and applications would be widely studied in the future.