Commensurate and incommensurate spin-density waves and the superconductivity dome in heavy electron systems

The nesting of the Fermi surfaces of an electron and a hole pocket separated by a nesting vector Q and the interaction between electrons gives rise to itinerant antiferromagnetism. The order can gradually be suppressed by mismatching the nesting and a quantum critical point is obtained as the Neel temperature tends to zero. If the vector Q is commensurate with the lattice (umklapp with Q = G/2), pairs of electrons can be transferred between the pockets and a superconducting dome above the quantum critical point may arise. If the vector Q is not commensurate with the lattice, there are eight phases that need to be considered: commensurate and incommensurate spin and charge density waves and four superconductivity phases, two of them with a modulated order parameter of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type. The renormalization group equations are studied and numerically integrated. The phase diagram is obtained as a function of the mismatch of the Fermi surfaces and the magnitude of vertical bar Q - G/2 vertical bar.