Commensurate and incommensurate SDW and the superconducting dome in heavy electron systems

A nested Fermi surface together with interactions between the carriers may give rise to itinerant AF. We consider an electron and a hole pocket, separated by a wave vector ${\bf Q}$, and Fermi momenta $k_{F1}$ and $k_{F2}$, respectively. The order is gradually suppressed by increasing the mismatch of the Fermi momenta and a QCP is obtained as $T_N \to 0$. If ${\bf Q} = {\bf G}/2$ (Umklapp), pairs of electrons can be transferred between the pockets. This process may lead to superconductivity and we investigate the conditions for a superconducting dome above the QCP [1]. If ${\bf Q} \neq {\bf G}/2$ eight phases need to be considered: commensurate and incommensurate SDW and CDW and four superconductivity phases, two of them with space modulated order parameter of the FFLO type with wave number $|{\bf Q} - {\bf G}/2|$. The RG equations are studied and a phase diagram with re-entrant SDW is obtained [2]. \vskip 0.05in \par\noindent [1] P. Schlottmann, Phys. Rev. B {\bf 89}, 014511 (2014). \par\noindent [2] P. Schlottmann, Phys. Rev. B {\bf 92}, 045115 (2015).