  Application of a perpendicular electric field induces a band gap in bilayer
graphene, and it also creates a "Mexican hat" structure in the dispersion
relation. This structure has unusual implications for the hydrogen-like bound
state of an electron to a Coulomb impurity. We calculate the ground state
energy of this hydrogen-like state as a function of the applied interlayer
voltage and the effective fine structure constant. Unlike in the normal
hydrogen atom, the resulting wavefunction has many nodes even in the ground
state. Further, the electron state undergoes "atomic collapse" into the Dirac
continuum both at small and large voltage.
