Hofstadter butterfly and quantum Hall effect in twisted double bilayer graphene

In this talk, I will discuss the energy spectrum and quantum Hall effect in twisted double bilayer graphene (TDBG, a pair of Bernal-stacked bilayer graphenes stacked with a rotational stacking fault). The electronic band structures of TDBG with AB-AB configuration and AB-BA configuration look similar in the absence of magnetic field, but their topological nature are different [1]. Therefore, the twins of AB-AB and AB-BA TDBG exhibit very different spectrum in magnetic field, by directly reflecting the difference in Chern numbers of the two pair structures [2]. For example, the first gap in the electron side of AB-AB TDBG remains opened in increasing magnetic fields, while that of AB-BA TDBG vanishes at some points due to the non-zero valley Chern number in AB-BA TDBG.
[1] M. Koshino, Phys. Rev. B 99, 235406 (2019).
[2] J. A. Crosse*, M. Koshino, P. Moon^†, in preparation.