We investigate the issues of competing orders and quantum criticality in cuprate superconductors via experimental studies of the high-field thermodynamic phase diagrams and the quasiparticle tunneling spectroscopy. Substantial field-induced quantum fluctuations are found in all cuprates investigated, and the corresponding correlation with quasiparticle spectra suggest that both electron- (n-type) and hole-doped (p-type) cuprate superconductors are in close proximity to a quantum critical point that separates a pure superconducting (SC) phase from a phase consisting of coexisting SC and a competing order. We further suggests that the relevant competing order is likely a spin-density wave (SDW) or a charge density wave (CDW), which can couple efficiently to an in-plane Cu-O bond stretching longitudinal optical (LO) phonon mode in the p-type cuprates but not in the n-type cuprates. This cooperative interaction may account for the pseudogap phenomenon above T, only in the p-type cuprate superconductors
