Magnetic impurity resonance states for different pairing symmetries in twisted bilayer graphene

Topology-Bounded Superfluid Weight in Twisted Bilayer Graphene

While regular flat bands are good for enhancing the density of states and hence the gap, they are detrimental to the superfluid weight. We show that the predicted nontrivial topology of the two lowest flat bands of twisted bilayer graphene (TBLG) plays an important role in the enhancement of the superfluid weight and hence of superconductivity. We derive the superfluid weight (phase stiffness) of the TBLG superconducting flat bands with a uniform pairing, and show that it can be expressed as an integral of the Fubini-Study metric of the flat bands. This mirrors results already obtained for nonzero Chern number bands even though the TBLG flat bands have zero Chern number. We further show that the metric integral is lower bounded by the topological C_{2z}T Wilson loop winding number of TBLG flat bands, which renders that the superfluid weight is also bounded by this topological index. In contrast, trivial flat bands have a zero superfluid weight. The superfluid weight is crucial in determining the Berezinskii-Kosterlitz-Thouless transition temperature of the superconductor. Based on the transition temperature measured in TBLG experiments, we estimate the topological contribution of the superfluid weight in TBLG.

Correlated insulating and superconducting states in twisted bilayer graphene below the magic angle

The emergence of flat bands and correlated behaviors in "magic angle" twisted bilayer graphene (tBLG) has sparked tremendous interest, though its many aspects are under intense debate. Here we report observation of both superconductivity and the Mott-like insulating state in a tBLG device with a twist angle of ~0.93°, which is smaller than the magic angle by 15%. At an electron concentration of ±5 electrons/moiré unit cell, we observe a narrow resistance peak with an activation energy gap ~0.1 meV. This indicates additional correlated insulating state, and is consistent with theory predicting a high-energy flat band. At doping of ±12 electrons/moiré unit cell we observe resistance peaks arising from the Dirac points in the spectrum. Our results reveal that the "magic" range of tBLG is in fact larger than what is previously expected, and provide a wealth of new information to help decipher the strongly correlated phenomena observed in tBLG.