Nematic order in twisted bilayer graphene by valley + spin fluctuation interference mechanism

In the magic angle twisted bilayer graphene (TBG), the nearly flat band emerges as a good platform of the strongly correlated electron systems. Especially, the C₃-symmetry-breaking nematic state observed in the TBG near the van Hove singularity (VHS) filling attracts increasing attention [1]. Here, we analyze the nematic state by focusing on the quantum interference mechanism, which was developed in the field of Fe-based superconductors [2]. We identify the nematic state in the TBG as the bond order [3], which is consistent with experiments. This nematic state originates from the interferences among the valley + spin fluctuations, due to the presence of the valley degrees of freedom and absence of the on-site Hund's coupling in the TBG.
We also discuss the time-reversal-symmetry-broken valley polarization involving a charge loop current near the nematic phase.
[1] A. Kerelsky et al., Nature 572, 95 (2019)
[2] S. Onari and H. Kontani, Phys. Rev. Lett. 109, 137001 (2012)
[3] S. Onari and H. Kontani, arXiv: 2011.01158 (2020)