Title: Phase evolution of Ce-based heavy-fermion superconductors under compression: a combined first-principle and effective-model study

Abstract: 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.