Composite orders and Lifshitz transition of heavy electrons

Magnetic and other unconventional electronic orders are discussed for heavy electrons. In addition to the ordinary Kondo lattice, we consider non-Kramers systems taking the two-channel Kondo lattice, and another lattice that consists of a singlet-triplet f² configuration. The latter gives a scalar order with staggered sublattices of crystalline-electric-field (CEF) and Kondo singlets, which accounts for the observed order in PrFe₄P₁₂. In the two-channel Kondo lattice, an oddfrequency pairing is realized that becomes degenerate at half-filling with a diagonal composite order involving both localized and conduction electrons. The degeneracy is interpreted in terms of a hidden SO(5) symmetry. For the ordinary Kondo lattice with exchange interaction J, we take insulating ground states as reference. The metallic states are approached by infinitesimal doping of carriers either from the Kondo insulator or from the antiferromagnetic insulator. By adding intersite exchange we find that location of the band extremum of the heavy band depends on the value of J. The change of J gives topological change of the Fermi surface, which corresponds to a generalized version of the Lifshitz transition, and occurs separately from the quantum critical point of the antiferromagnetic order.