Long-range quantum entanglement in metals

Long-range quantum entanglement is now understood to be a fundamental characteristic of exotic states of quantum matter with an energy gap to all excitations: these include the fractional quantum Hall states found at very high magnetic fields, and certain insulators with possible spin-liquid states. However, such entanglement can also be present in gapless, conducting states of matter (‘metals’ ) found under more ordinary conditions. I will describe recent experiments on the cuprate compounds, and on graphene, which are consistent with the presence of novel metallic states with long-range entanglement.