Moiré Magic*

Moiré materials are formed when two-dimensional crystals are overlaid with a small difference in lattice constant or orientation. When the two-dimensional crystals are semimetals or semiconductors, the low energy states of moiré materials are described by periodic continuum models and have the electronic properties of artificial crystals with lattice constants on the tens of nanometer scale, allowing the number of electrons per atom to be varied widely. My talk will focus on the particular case of graphene bilayers, which exhibit a rich set of strongly correlated electron states, including superconductors and orbital magnets, when twisted close to a magic relative orientation angle at which the electron velocity at the Fermi level vanishes. Electronic correlations in Magic Angle Twisted Bilayer Graphene (MAtBG) are strong because the low-energy moiré superlattice bands are very narrow, and unusual becasue of non-trivial band topology inherited from the isolated layer Dirac cones. I will discuss efforts in my group at the University of Texas to settle on answers to some of the following questions. Does the flat-band dispersion that remains near the magic twist angle play a key role in controlling the phase diagram? Why are insulating states at odd integer filling factors not always Chern insulators? Is superconductivity in MAtBG mediated by electron-phonon interactions, by quantum fluctuations of spin/valley/orbital degrees of freedom, or by some other mechanism? What is the pair wavefunction for Cooper pairs in MAtBG? Are there important similarities between the doped Mott insulator states of cuprates and MAtBG states close to integer moiré band filling?