▎ 摘　　要

We study the energy spectrum of a graphene bilayer in the presence of transverse electric and magnetic fields. We find that the resulting Landau levels exhibit a nonmonotonic dependence on the electric field, as well as numerous level crossings. This behavior is explained using quasiclassical quantization rules that properly take into account the pseudospin of the quasiparticles. The pseudospin generates the Berry phase, which leads to a shift in energy quantization and results in a pseudo-Zeeman effect. The latter depends on the electric field, alternates in sign among the two valleys, and also reduces the band gap. Analytic formulas for other pseudospin-related quantities, such as the anomalous Hall conductivity, are derived and compared with prior theoretical work.