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The eigenstates of an electron in the chiral two-dimensional electron gas(C2DEG) formed in an AB-stacked bilayer or an ABC-stacked trilayer graphene isa spinor with $4$ or $6$ components respectively. These components give theamplitude of the wave function on the $4$ or $6$ carbon sites in the unit cellof the lattice. In the tight-binding approximation, the eigenenergies are thusfound by diagonalizing a $4\times 4$ or a $6\times 6$ matrix. In the continuumapproximation where the electron wave vector $% k<<1/a_{0},$ with $a_{0}$ thelattice constant of the graphene sheets, a common approximation is the two-bandmodel\cite{McCann2006} (2BM)\ where the eigenstates for the bilayer andtrilayer systems are described by a two-component spinor that gives theamplitude of the wave function on the two sites with low-energy $\left\vertE\right\vert <<\gamma_{1}$ where $% \gamma_{1}$ is the hopping energy betweensites that are directly above one another in adjacent layers. The 2BM has beenused extensively to study the phase diagram of the C2DEG in a magnetic field aswell as its transport and optical properties. In this paper, we use a numericalapproach to compute the eigenstates and Landau level energies of the fulltight-binding model in the continuum approximation and compare them with theprediction of the 2BM when the magnetic field or an electrical bias between theoutermost layers is varied. Our numerical analysis shows that the 2BM is a goodapproximation for bilayer graphene in a wide range of magnetic field and biasbut mostly for Landau level $M=0.$ The applicability of the 2BM in trilayergraphene, even for level $M=0,$ is much more restricted. In this case, the 2BM\fails to reproduce some of the level crossings that occur between thesub-levels of $M=0.$

Validity of the two-band model of bilayer and trilayer graphene in a magnetic field