Echolocation of Scatterers by Quasiparticles in Cuprate Superconductors

How much can STM techniques tell us about the realization of disorder in a particular sample under study? We propose a new method of STM-data analysis which allows for the determination of the position and strength of impurities/scatterers. Furthermore, for cuprates, it can potentially be used to distinguish if the scatterer is ``ordinary'' or ``anomalous"~\footnote{T. S. Nunner et al, Phys. Rev. B, \textbf{73}, 104511 (2006)}, i.e. part of the pairing potential. The method relies on quasiparticle interference \footnote{Q. Wang and D.-H.~Lee, Phys. Rev. B \textbf{67}, 020511 (2003)} as observed in cuprates$^3$. As for much of the STM phenomenology in cuprates$^{1-3}$, our starting point is the existence of well-defined Bogoliubov quasiparticles defined by a quadratic phenomenological Hamiltonian with intrinsic disorder. By \emph{Energy} ``Fourier-Transform''ing the measured local density of states (LDOS) spectrum from a single point, one can extract the ``echo'' time that a quasiparticle takes to go to and return from a nearby scatterer; doing this at several points in a local patch allows a ``sonar''-like echolocation of the scatterer. This method is complementary to Fourier-Transform Scanning Tunneling Spectroscopy \footnote{K. McElroy et al, Nature, \textbf{422}, 592 (2003)} wherein \emph{Space} Fourier transforms of LDOS data yield the quasiparticle dispersion.