Extracting phase information about the superconducting order parameter from defect bound states

Impurity bound states and quasi-particle scattering from these can serve as sensitive probes for identifying the pairing state of a superconducting condensate. We introduce and discuss defect bound state quasi-particle interference (DBS-QPI) imaging as a tool to extract information about the symmetry of the order parameter from spatial maps of the density of states around magnetic and non-magnetic impurities. We show that the phase information contained in the scattering patterns around impurities can provide valuable information beyond what is obtained through conventional QPI imaging. Keeping track of phase, rather than just magnitudes, in the Fourier transforms is achieved through phase-referenced Fourier transforms that preserve both real and imaginary parts of the QPI images. We further compare DBS-QPI to other approaches which have been proposed to use either QPI or defect scattering to distinguish different symmetries of the order parameter.