▎ 摘　　要

It has been shown that Bernal stacked bilayer graphene (BLG) in a uniform magnetic field demonstrates integer quantum Ha l l effect with a zero Landau-level anomaly (Novoselov et al., 2006). In this article we consider such system in a two dimensional periodic magnetic modulation with square lattice symmetry. It is shown algebraically that the resulting Hofstadter spectr u m can be expressed in terms of the corresponding spectrum of monolayer graphene in a similar magnetic modulation. In the weak-field limit, using the tight-binding model, we also derive the Harper-Hofstadter equation for such BLG system in a periodic magnetic modulation. We f urther demonstrate the topological quantisation of Ha l l conductivity in such system and point out that the quantised Ha l l plateaus are equally spaced for a l l quantu m numbers for the quantised Ha l l conductivity.