This paper presents a study of the electronic band structure of bilayer graphene with an asymmetry gap $ \Delta $ between the conduction and valence bands, caused by a potential difference between the layers. A tight-binding model is used to calculate the band structure, with a self-consistent Hartree approximation to account for imperfect screening of an external gate, which controls the electron density $ n $ on the bilayer. The asymmetry gap $ \Delta(n) $ depends on the density $ n $, and the paper discusses its influence on the quantum Hall effect observations. The low-energy Hamiltonian for bilayer graphene describes chiral quasiparticles with a parabolic dispersion and Berry phase $ 2\pi $, in contrast to monolayer graphene with a Dirac-like dispersion and Berry phase $ \pi $. The asymmetry gap $ \Delta $ is influenced by the screening of an additional transverse electric field, leading to a finite asymmetry gap $ \Delta(0) $ at zero excess density. The paper analyzes the effect of this asymmetry on the cyclotron mass and the sequence of quantum Hall effect plateaus at low density. The electronic densities $ n_1 $ and $ n_2 $ on the individual layers are calculated using an integral over the Fermi surface. The self-consistent calculation begins with zero external gate voltage and evaluates the gap $ \Delta(0) $ using equations derived from the model. The results show that the asymmetry gap $ \Delta(n) $ depends on the bare asymmetry $ \Delta_0 $, and the screening effectiveness $ \Lambda $, which depends on the model parameters. The paper also discusses the influence of the asymmetry gap $ \Delta_0 $ on the cyclotron mass $ m_c $, which is measured in experiments such as Shubnikov de Haas oscillations. The cyclotron mass is found to be asymmetric for positive and negative densities, with divergent behavior at low density due to the "mexican hat" structure of the low-energy bands. The asymmetry gap $ \Delta_0 $ also affects the sequence of quantum Hall effect plateaus. The Landau level (LL) spectrum of bilayer graphene is analyzed, showing that the asymmetry gap leads to a plateau at zero density in the Hall conductivity. The temperature dependence of this plateau is different from other plateaus due to different activation energies related to $ \Delta(0) $ and $ \hbar\omega_c $. The paper concludes that the asymmetry gap $ \Delta(0) $ can influence observations of the integer quantum Hall effect by introducing a plateau at zero density in the Hall conductivity. This plateau is accompanied by a dip in the diagonal conductivity, and the temperature dependence of the plateau can be used to extract the value of the asymmetry gap $ \Delta(0) $. This is distinguishable from the behavior of higher plateaus, which are determined byThis paper presents a study of the electronic band structure of bilayer graphene with an asymmetry gap $ \Delta $ between the conduction and valence bands, caused by a potential difference between the layers. A tight-binding model is used to calculate the band structure, with a self-consistent Hartree approximation to account for imperfect screening of an external gate, which controls the electron density $ n $ on the bilayer. The asymmetry gap $ \Delta(n) $ depends on the density $ n $, and the paper discusses its influence on the quantum Hall effect observations. The low-energy Hamiltonian for bilayer graphene describes chiral quasiparticles with a parabolic dispersion and Berry phase $ 2\pi $, in contrast to monolayer graphene with a Dirac-like dispersion and Berry phase $ \pi $. The asymmetry gap $ \Delta $ is influenced by the screening of an additional transverse electric field, leading to a finite asymmetry gap $ \Delta(0) $ at zero excess density. The paper analyzes the effect of this asymmetry on the cyclotron mass and the sequence of quantum Hall effect plateaus at low density. The electronic densities $ n_1 $ and $ n_2 $ on the individual layers are calculated using an integral over the Fermi surface. The self-consistent calculation begins with zero external gate voltage and evaluates the gap $ \Delta(0) $ using equations derived from the model. The results show that the asymmetry gap $ \Delta(n) $ depends on the bare asymmetry $ \Delta_0 $, and the screening effectiveness $ \Lambda $, which depends on the model parameters. The paper also discusses the influence of the asymmetry gap $ \Delta_0 $ on the cyclotron mass $ m_c $, which is measured in experiments such as Shubnikov de Haas oscillations. The cyclotron mass is found to be asymmetric for positive and negative densities, with divergent behavior at low density due to the "mexican hat" structure of the low-energy bands. The asymmetry gap $ \Delta_0 $ also affects the sequence of quantum Hall effect plateaus. The Landau level (LL) spectrum of bilayer graphene is analyzed, showing that the asymmetry gap leads to a plateau at zero density in the Hall conductivity. The temperature dependence of this plateau is different from other plateaus due to different activation energies related to $ \Delta(0) $ and $ \hbar\omega_c $. The paper concludes that the asymmetry gap $ \Delta(0) $ can influence observations of the integer quantum Hall effect by introducing a plateau at zero density in the Hall conductivity. This plateau is accompanied by a dip in the diagonal conductivity, and the temperature dependence of the plateau can be used to extract the value of the asymmetry gap $ \Delta(0) $. This is distinguishable from the behavior of higher plateaus, which are determined by