  The tilted balance among competing interactions can yield a rich variety of
ground states of quantum matter. In most Ce-based heavy fermion systems, this
can often be qualitatively described by the famous Doniach phase diagram, owing
to the competition between the Kondo screening and the
Ruderman-Kittel-Kasuya-Yoshida exchange interaction. Here, we report an unusual
pressure-temperature phase diagram beyond the Doniach one in CeCuP2. At ambient
pressure, CeCuP2 displays typical heavy-fermion behavior, albeit with a very
low carrier density. With lowering temperature, it shows a crossover from a non
Fermi liquid to a Fermi liquid at around 2.4 K. But surprisingly, the Kondo
coherence temperature decreases with increasing pressure, opposite to that in
most Ce-based heavy fermion compounds. Upon further compression, two
superconducting phases are revealed. At 48.0 GPa, the transition temperature
reaches 6.1 K, the highest among all Ce-based heavy fermion superconductors. We
argue for possible roles of valence tuning and fluctuations associated with its
special crystal structure in addition to the hybridization effect. These
unusual phase diagrams suggest that CeCuP2 is a novel platform for studying the
rich heavy fermions physics beyond the conventional Doniach paradigm.
