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We investigate the full doping and strain-dependent phase diagram of the normal state of magic-angle twisted bilayer graphene (TBG). Using comprehensive Hartree-Fock calculations, we show that at temperatures where superconductivity is absent the global phase structure can be understood based on the competition and coexistence between three types of intertwined orders: a fully symmetric phase, spatially uniform flavor-symmetry-breaking states, and an incommensurate Kekulé spiral (IKS) order. For small strain, the IKS phase, recently proposed as a candidate order at all nonzero integer fillings of the moiré unit cell, is found to be ubiquitous for noninteger doping as well. We demonstrate that the corresponding electronic compressibility and Fermi surface structure are consistent with the "cascade" physics and Landau fans observed experimentally. This suggests a unified picture of the phase diagram of TBG in terms of IKS order.

Nodal semimetals are a unique platform to explore topological signatures of the unusual band structure that can manifest by accumulating a nontrivial phase in quantum oscillations. Here we report a study of the de Haasvan Alphen oscillations of the candidate topological nodal line semimetal CaAgAs using torque measurements in magnetic fields up to 45 T. Our results are compared with calculations for a toroidal Fermi surface originating from the nodal ring. We find evidence of a nontrivial π phase shift only in one of the oscillatory frequencies. We interpret this as a Berry phase arising from the semi-classical electronic Landau orbit which links with the nodal ring when the magnetic field lies in the mirror (ab) plane. Furthermore, additional Berry phase accumulates while rotating the magnetic field for the second orbit in the same orientation which does not link with the nodal ring. These effects are expected in CaAgAs due to the lack of inversion symmetry. Our study experimentally demonstrates that CaAgAs is an ideal platform for exploring the physics of nodal line semimetals and our approach can be extended to other materials in which trivial and nontrivial oscillations are present.

We uncover topological features of neutral particle-hole pair excitations of correlated quantum anomalous Hall (QAH) insulators whose approximately flat conduction and valence bands have equal and opposite nonzero Chern number. Using an exactly solvable model we show that the underlying band topology affects both the center-of-mass and relative motion of particle-hole bound states. This leads to the formation of topological exciton bands whose features are robust to nonuniformity of both the dispersion and the Berry curvature. We apply these ideas to recently reported broken-symmetry spontaneous QAH insulators in substrate aligned magic-angle twisted bilayer graphene.