Microscopic theory of multi-stage Fermi surface reconstruction in heavy fermion systems with quartet multipolar local moments

Recent experiments on Ce₃Pd₂₀(Si,Ge)₆ show novel quantum critical behaviors associated with two consecutive quantum phase transitions upon varying the external magnetic field. Interestingly, the derivative of the Hall conductivity shows a discontinuous jump at each phase transition, which was attributed to sequential Fermi surface reconstructions. Motivated by this discovery and previous theory work, we consider a microscopic model of itinerant electrons coupled to the local moments described by a quartet of ground states in a crystal-electric-field (CEF). Such a quartet arises due to two degenerate Kramers doublets of Ce³⁺ ions in a cubic CEF and supports a large number of dipolar, quadrupolar, and octupolar moments. Specifically, we investigate emergent quantum phase transitions and criticality in a local effective model, the so-called Bose-Fermi Kondo model. This model describes the competition between the Kondo effect with the itinerant electrons and RKKY interaction for all of the 15 symmetry-allowed multipolar moments. Using renormalization group analyses, we demonstrate that a multitude of quantum phase transitions can occur depending on which multipolar moments participate in the Fermi surface formation and which other multipolar moments are decoupled via Kondo destruction. We provide a concrete example of two consecutive quantum phase transitions that involve the quadrupolar and dipolar/octupolar moments at two different stages. Our work provides an illuminating insight as to the importance of local symmetries in understanding multipolar Kondo lattice systems and an outlook for future directions.