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. LaPt2Ge2 undergoes a tetragonal-to-monoclinic structural phase transition (SPT) at T-s = 394 K, accompanying a double period modulation in the a-axis direction, and superconducts at T-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 Pt-195-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-s and increasing T-c in LaPt2-xGe2+x. Comparison of La-139- and Pt-195-NMR data reveals moderate fluctuations associated with SPT. From La-139-NQR measurements at zero field, we found that an isotropic superconducting gap is realized in LaPt2-xGe2+x (x = 0.20). We discuss the relationship between superconductivity and the SPT order/fluctuations.
