  We present scanning tunneling spectroscopic and high-field thermodynamic
studies of hole- and electron-doped (p- and n-type) cuprate superconductors.
Our experimental results are consistent with the notion that the ground state
of cuprates is in proximity to a quantum critical point (QCP) that separates a
pure superconducting (SC) phase from a phase comprised of coexisting SC and a
competing order, and the competing order is likely a spin-density wave (SDW).
The effect of applied magnetic field, tunneling current, and disorder on the
revelation of competing orders and on the low-energy excitations of the
cuprates is discussed.
