Theoretical study ofChern transitions in Hofstadter bands of twisted double bilayer graphene*

We study Hofstadter physics of twisted double bilayer graphene (TDBG) in presence of an out-of-plane electric field. In this system Hofstadter bands have unequal distribution of charges in the layers. Moreover, such layer polarization depends on the valley index. These together lead to non-trivial changes of Chern number as a function of the applied electric field. In addition, if we include an assumed spin-exchange, the resulting cascade of even and odd change of Chern numbers matches with the experimental findings. This talk will focus on the theoretical analysis of the work, where the experimental results will be presented in a separate talk.