Topological materials discovery from crystal symmetry

Topological materials discovery has evolved at a rapid pace over the past 15 years following identification of first nonmagnetic topological insulators (TIs), crystalline (TCIs), and 3D semimetals (TSMs). Most recently, through complete analyses symmetry-allowed band structures - including theory Quantum Chemistry (TQC) researchers have determined crystal-symmetry-enhanced Wilson-loop symmetry-based indicators for phases, leading to higher-order TCIs TSMs. The recent application TQC related methods high-throughput revealed that half all known stoichiometric, solid-state, are Fermi level, 85% stoichiometric host energetically isolated bands, just under $2/3$ bands in carry stable topology TI or TCI. In this Review, we survey electronic solids from prediction 2D TIs recently introduced facilitated large-scale searches materials. We also discuss future venues manipulation solid-state charge-density-wave compounds, magnetic materials, few-layer devices.