  We study a magnetic impurity intercalated in bilayer graphene. A
representative configuration generates a hybridization function with strong
dependence on the conduction-electron energy, including a full gap with one
hard and one soft edge. Shifts of the chemical potential via gating or doping
drive the system between non-Kondo (free-moment) and Kondo-screened phases,
with strong variation of the Kondo scale. Quantum phase transitions near the
soft edge are of Kosterlitz-Thouless type, while others are first order. Near
the hard edge, a bound-state singlet appears inside the gap; although of
single-particle character, its signatures in scanning tunneling spectroscopy
are very similar to those arising from a many-body Kondo resonance.
