Inferring effective interactions from the local density of states: Application to STM data from Bi2 Sr2 Ca Cu2 O8+δ

While the influence of impurities on the local density of states (LDOS) in a metal is notoriously nonlocal due to interference effects, low-order moments of the LDOS in general can be shown to depend only on the local structure of the Hamiltonian. Specifically, we show that an analysis of the spatial variations of these moments permits one to work backward from scanning tunneling microscopy (STM) data to infer the local structure of the underlying effective Hamiltonian. Applying this analysis to STM data from the high-temperature superconductor Bi2 Sr2 Ca Cu2 O8+δ, we find that the variations of the electrochemical potential are remarkably small (i.e., the disorder is, in a sense, weak) but that there are large variations in the local magnitude of the d -wave gap parameter.