(Top left) Atomic arrangement in bilayer graphene, with the two main hopping parameters, γ0 and γ1, between carbon π orbitals within and between layers, respectively. (Top right) Electronic bands of bilayer graphene. Single-layer graphene features Dirac cones with sharp neutrality points, whereas bilayer graphene exhibits parabolic dispersion as shown. There are two valence and conduction bands, as each layer contributes with one set of bands. (Bottom) Feynman diagrams, such as the example shown, are used to calculate the electron-hole polarizability. This diagram depicts the dynamics of an electron-hole pair, obtained from the convolution of electron (red) and hole (blue) propagators. The calculation gives gives a logarithmically divergent polarizability.