Quantum oscillations: Butterflies on a superlattice

Quantum oscillations refers to the periodic behaviour observed in observables of many materials such as resistivity or magnetisation under the effects of an external magnetic field. Because the period of the oscillations can be related to the area of the Fermi surface perpendicular to the magnetic field, this technique has been widely employed to map Fermi surfaces. In this talk, I will review the classic theory of quantum oscillations, and develop this for the resistivity of a two-dimensional system: twisted double-bilayer graphene. Here, in addition to the quantum oscillatory behaviour of the resistivity with the magnetic fields at very low energies, there is an additional mechanism for quantum oscillations caused by the interference effect of electrons travelling through a Kagome network of trajectories in reciprocal space.