Superconductivity and the electronic phase diagram of LaPt$_{2-x}$Ge$_{2+x}$

In many cases, unconventional superconductivity are realized by suppressing another order parameter, such as charge density wave (CDW) or spin density wave (SDW). This suggests that the fluctuations of these order parameters play an important role in producing superconductivity. LaPt$_2$Ge$_2$ undergoes a tetragonal-to-monoclinic structural phase transition (SPT) at $T_{\rm s}$ = 394 K, accompanying a double period modulation in the $a$-axis direction, and superconducts at $T_{\rm c}$ = 0.41 K. We performed band calculations and found 2D (two dimensional)-like Fermi surfaces with partial nesting. A reduction in the density of states in the monoclinic phase was found in the calculation and confirmed by $^{195}$Pt-NMR. We suggest a CDW as a possible cause for the SPT. By changing the stoichiometry between Pt and Ge, we succeeded in suppressing $T_{\rm s}$ and increasing $T_{\rm c}$ in LaPt$_{2-x}$Ge$_{2+x}$. Comparison of $^{139}$La- and $^{195}$Pt-NMR data reveals moderate fluctuations associated with SPT. From $^{139}$La-NQR measurements at zero field, we found that an isotropic superconducting gap is realized in LaPt$_{2-x}$Ge$_{2+x}$ ($x$ = 0.20). We discuss the relationship between superconductivity and the SPT order/fluctuations.