  We consider a spin-1/2 Heisenberg chain coupled via a Kondo interaction to
two-dimensional Dirac fermions. The Kondo interaction is irrelevant at the
\textit{decoupled} fixed-point, leading to the existence of a Kondo-breakdown
phase and a Kondo-breakdown critical point separating such a phase from a heavy
Fermi liquid. We reach this conclusion on the basis of a renormalization group
analysis, large-N calculations as well as extensive auxiliary-field quantum
Monte Carlo simulations. We extract quantities such as the zero-bias tunneling
conductance which will be relevant to future experiments involving adatoms on
semimetals such as graphene.
