Prize Talk: Oliver E. Buckley Condensed Matter Prize II: The unreasonable effectiveness of topology in the science of quantum materials*

Topological concepts have played an unexpectedly pivotal role in the field of quantum materials. In this talk I will briefly revisit various examples that transcend the established notions of topology in band insulators, including extensions to the gapless regime such as Weyl and Dirac semimetals, and explorations beyond the independent electron approximation. I will also discuss some exciting recent developments in moire' materials where band geometry and topology lead to new collective properties and stabilize fractional Hall states at zero magnetic field. Finally, I will highlight hidden connections that were found between seemingly distinct topological phenomena, the key role played by many-body quantum entanglement in propelling conceptual progress and conclude with some open directions in this field.