Ripples on a D-wave Sea: Quasiparticle Wavefunction Imaging in Cuprate Superconductors J. C. Séamus Davis, Cornell University

High temperature superconductivity in the cuprates emerges when the localized electrons of a Mott-insulator become itinerant due to carrier-doping. Understanding both the electronic ground state and the excited states of these systems are key challenges in CM physics today. Angle-resolved photoemission (ARPES) studies have been remarkably successful in mapping the momentum-space characteristics of the cuprate excited states. However, since cuprate superconductivity develops from atomically localized electrons and exhibits nanoscale disorder, a pure momentum-space description may not be sufficient. Instead, simultaneous information on electronic structure in both the real-space and momentum-space may be required. I will describe a combination of novel scanning tunneling microscopy (STM) techniques which achieves these apparently contradictory aims. The first technique, atomic-resolution spectroscopic mapping, allows imaging of interactions between quasiparticle states and the real-space environment at the atomic-scale. For example, the wavefunctions and energy-levels of local electronic states at individual impurity atoms can be measured . More recent advances with this technique include the discovery of complex spatial variations in the superconducting electronic structure at the nanoscale . A second technique, Fourier-transform scanning tunneling spectroscopy (FT-STS), is used to study interference patterns of the delocalized wavelike electronic states. For optimally doped samples, analysis of these patterns as due to quasiparticle interference , yields  the Fermi surface and the d-wave superconducting energy gap | |, in excellent agreement with ARPES. Finally I will describe FTSTS experiments designed to detect and identify the electronic ground state in other regions of the cuprate phase diagram including studies of the vortex core  and of strongly underdoped samples.   Science 285, 88 (1999); Nature 403, 746 (2000); Nature 411 920 (2001).   Nature 413 282 (2001);  Nature 415, 412 (2002).   Byers J. M., Flatté M. E., Scalapino D. J., Phys. Rev. Lett. 71, 3363 (1993); Wang Q. and Lee D.-H., Phys. Rev. B 67 020511 2003;   Science 297 1148 (2002); Nature 422, 592 (2003).   Science 266, 455 (2002).