Spectroscopic imaging STM studies of high-T_C superconductivity

Since its discovery in 1986, understanding both the ground state and excited states of high temperature superconductivity (HTSC) has been one of the main challenges in modern condensed matter physics. One remarkable observation in HTSC cuprates is that the superconductivity appears as the localized electrons of a Mott insulator become itinerant due to carrier doping. Momentum sensitive probes like Angle Resolved Photo-Emission Spectroscopy (ARPES) and Inelastic Neutron Scattering (INS) have played important roles in mapping the momentum-space properties of the cuprate electronic structure. However, considering that cuprate superconductivity develops from atomically localized electrons and shows nanoscale disorder, a purely momentum dependent description is far from sufficient. Here, we describe novel spectroscopic imaging scanning tunneling microscopy (SI-STM) studies, which can probe the real-space electronic structure at the nano-scale, along with momentum-space electronic structure. We discuss a series of recent results from SI-STM studies of Bi₂Sr ₂CaCu₂O_8+x and Ca_2-xNa _xCuO₂Cl₂.