  Unconventional superconductivity frequently emerges as the transition
temperature of a magnetic phase, typically antiferromagnetic, is suppressed
continuously toward zero temperature. Here, we report contrary behavior in
pressurized CeRhGe3, a non-centrosymmetric heavy fermion compound. We find that
its pressure-tuned antiferromagnetic transition temperature (TN) appears to
avoid a continuous decrease to zero temperature by terminating abruptly above a
dome of pressure-induced superconductivity. Near 21.5 GPa, evidence for TN
suddenly vanishes, the electrical resistance becomes linear in temperature and
the superconducting transition reaches a maximum. In light of X-ray absorption
spectroscopy measurements, these characteristics appear to be related to a
pressured-induced Ce valence instability, which reveals as a sharp increase in
the rate of change of Ce valence with applied pressure.
