Excitons without effective mass: Biased bilayer graphene

Understanding the dynamics of excitons in two-dimensional semiconductors requires a theory that incorporates the essential physics distinct from their three-dimensional counterparts. In addition to the modified dielectric environment, single-particle states with strongly nonparabolic dispersion appear in many two-dimensional band structures, so that ``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 semianalytic theory used to investigate the properties of ground and excited excitonic states. This includes determination of relative oscillator strengths and magnetic moments (valley $g$-factors) which can be directly compared to recent experimental measurements.