Excitons beyond the effective mass approximation: application to biased bilayer graphene

In conventional semiconductors, the exciton bound state (arising from the attractive Coulomb interaction between electrons and holes) can be successfully analyzed by the effective mass approximation based on the lowest-order parabolic dispersion relation at band extrema. However, parabolic dispersion is by no means the only possible outcome endowed by a periodic lattice potential, especially in two dimensional electronic materials, where weak inter-subband matrix elements suppress otherwise strong band repulsion across a forbidden gap, resulting in nonparabolic ‘Mexican hat’ or ‘caldera’-shaped bands, in which “effective mass” is ill-defined. Focusing on electrostatically-biased bilayer graphene as an example where quartic (and higher) dispersion terms are necessary, we present a semi-analytic theory used to investigate the properties of ground and excited excitonic states. This includes determination of the exciton binding energy and wavefunctions, which are further used to analyze the relative oscillator strengths and magnetic moments (g-factors) that can be directly compared to recent experimental measurements.