Researchers build a framework to find quantum invariants systematically

Seishiro Ono of the University of Tokyo and Ken Shiozaki of Kyoto University have developed a systematic framework for constructing topological invariants, offering a new approach to identifying exotic materials. While symmetry-indicator theory and topological quantum chemistry have aided materials discovery, the researchers’ method addresses limitations by characterizing topological phases beyond the reach of those existing frameworks. Their work, based on the Atiyah-Hirzebruch spectral sequence in momentum space, notably constructs invariants for time-reversal symmetric spinful superconductors, systems previously undetectable by symmetry indicators. The resulting topological invariants completely characterize K-groups in 159 space groups. The construction of topological invariants, mathematical…