SCANNING TUNNELING MICROSCOPY OF THE

The cuprate superconductors remain an enigma after nearly 20 years of research. Al-though most of their properties in the superconducting state can be attributed to d-wave superconducting order with a short coherence length, very little else about them is under-stood. In particular, the nature of the electronic state outside the superconducting phase remains controversial. Whether the anamolous 'normal ' state properties of the cuprate super-conductors are the result of some remnant of superconductivity or some competing electronic order, and whether these properties in uence superconductivity, remain perhaps the most important unanswered questions in the eld. Because the superconducting phase and many of the proposed normal phases have variations in their electronic structure on atomic length scales, a local probe with atomic spatial resolution could be very useful in understanding the electronic properties of the cuprates. In this thesis, we will exploit the ability of Scanning Tunneling Microscopy (STM) to measure the density of states on an atomic length scale to study both the superconduct-ing and normal state of the high temperature superconductor Bi2Sr2CaCu2O8+. In the superconducting state, we have found a novel signature of d-wave superconductivity- cer