  Superconductivity in FeSe is strongly enhanced under applied pressure and it
is proposed to emerge from anomalously coupled structural and magnetic phases.
Small impurities inside the Fe plane can strongly disrupt the pair formation in
FeSe at ambient pressure and can also reveal the interplay between normal and
superconducting phases. Here, we investigate how an impurity inside the Fe
plane induced by the Cu substitution can alter the balance between competing
electronic phases of FeSe at high pressures. In the absence of an applied
magnetic field, at low pressures the nematic and superconducting phases are
suppressed by a similar factor. On the other hand, at high pressures, above 10
kbar, the superconductivity remains unaltered despite the lack of any signature
in transport associated to a magnetic phase in zero-magnetic field. However, by
applying a magnetic field, the resistivity displays an anomaly preceding the
activated behaviour in temperature, assigned to a magnetic anomaly. We find
that the high-pressure superconducting phase of FeSe is robust and remains
enhanced in the presence of Cu impurity, whereas the magnetic phase is not.
This could suggest that high-$T_{\rm c}$ superconductivity has a
sign-preserving order parameter in a presence of a rather glassy magnetic
phase.
