Investigation of Competing Orders and Quantum Criticality in Cuprate Superconductors using Scanning Tunneling Microscopy

The existence of competing orders in cuprate superconductors and their proximity to quantum criticality give rise to a variety of non-universal phenomena. To investigate this issue, we study the quasi-particle tunneling spectra of various cuprates with a low- temperature scanning tunneling microscope. Specifically, we will present the temperature evolution and the spatial variation of the quasi-particle tunneling spectra of the \emph{s}-wave pairing electron-doped infinite-layer $Sr_{0.9}La_{0.1}CuO_2$ and the \emph{d}-wave pairing optimally hole-doped $YBa_2Cu_3O_x$. We will compare the spectroscopy with bulk magnetic measurements as a function of applied field and discuss the physics implication.