Disorder and quasiparticle interference in high-Tc superconductors

Synopsis

In the past two decades, two developments have spurred new interest in atomic-scale effects in superconductors. The first is the discovery of systems, such as the high-Tc cuprates, heavy fermion, and iron-based superconductors, with very short coherence lengths, which in the cuprates even approach the unit cell size. The second is the ability to image atomic-scale features in scanning tunneling microscopy (STM). Comparison of such images with theory has sometimes been frustrating, since STM images typically contain much more detail than that predicted by current theoretical calculations for lattice models. In this talk I first discuss the marriage of first-principles electronic structure theory with phenomenological theories of superconductivity to calculate images of high-Tc superconducting surfaces within so-called Bogoliubov-de Gennes-Wannier (BdG-W) theory,  and show how this  approach can naturally explain a host of longstanding puzzles in STM images of cuprates and, more recently, iron-based superconductors.  I then review the notion of quasiparticle interference (QPI) or Fourier transform scanning spectroscopy, whereby disorder can enable one to deduce key properties of electronic structure near the Fermi level, including the superconducting gap. One can improve quantitative understanding of QPI maps in unconventional superconductors using the  BdG-W theory, but it is more interesting to ask qualitative questions, for instance if one can use the technique to definitively decide whether or not a novel superconductor has a gap which changes sign over the Fermi surface.