High-temperature superconductivity in the cuprates emerges when the localized electrons of a Mott insulator become mobile due to carrier doping. Understanding both the electronic ground state and the excited states of these systems are key challenges in physics today. Angle-resolved photoemission spectroscopy (ARPES) and inelastic neutron-scattering (INS) studies have been remarkably successful in mapping the momentum-space characteristics of the cuprate electronic structure. However, since cuprate superconductivity develops from atomically localized electrons and exhibits nanoscale disorder, a pure momentum-space description is unlikely to be sufficient. Instead, simultaneous information on electronic structure at the nanoscale in real space, and throughout momentum space, is required. Here, we describe a combination of novel spectroscopic imaging scanning tunneling microscopy (SI-STM) techniques that we have developed to achieve these apparently contradictory aims, along with the outcome of a series of SI-STM studies of the electronic structure of Bi2Sr2CaCu2O8+x.
