  In many Ce-based superconductors, superconducting (SC) phases emerge or can
be tuned in proximity to the antiferromagnetic (AF) quantum critical point
(QCP), but so far the explicit phase evolution near the QCP lack theoretical
understanding. Here, by combing the density functional theory plus dynamical
mean-field theory (DFT+DMFT) with effective-model calculations, we provide a
theoretical description for Ce-based superconductors under compression.
DFT+DMFT calculations for the normal states reveal that the Kondo
hybridizations are significantly enhanced under compression, while the
initially localized $f$ electrons become fully itinerant via
localized-itinerant crossover. We then construct an effective model and show
that with the extracted Kondo coupling and RKKY exchange strengths from
first-principle calculations, the ground-state phases of these materials can be
properly predicted. We also show that the coexistence of magnetic correlation
and Kondo hybridization can drive AF+SC coexisting state in narrow compression
region. Under compression, competition between Kondo and RKKY interactions can
drive successive transitions, from AF phase to AF+SC coexisting phase, then to
paramagnetic SC phase via an AF transition which generates the QCP, and finally
to normal Kondo paramagnetic (KP) phase through an SC-KP transition induced by
the localized-itinerant crossover. Our study gives proper explanation to the
pressure-induced QCP and SC-KP transition, and to the phase evolution in
pressured Ce-based superconductors, and can help to understand the SC states
around the ferromagnetic quantum transition points in uranium-based
superconductors.
