Qualitative Analysis of Quasiparticle Interference Using Feynman Parametrization*

Quasiparticle interference (QPI) is observed in Scanning Tunneling Spectroscopy (STS) where an impurity causes oscillating patterns of the local density of states (LDOS) [1].Green's function methods commonly used to simulate QPI [2-4] often show disagreement with experiments, especially when computing inter-band scattering. Motivated by our own STS data [5] on Fe-based superconductors we developed a new scheme to help experimentalists to qualitatively analyze the calculated QPI. It relies on Feynman parametrization (FP), a technique widely used in quantum field theory for loop evaluation. We show that the interband QPI problem can be represented by a collection of new 'intermediate bands' possessing relatively easier geometries. We discuss two example applications. First, the QPI between two quadratic bands, where IBA predicts DOS divergences at momentum values that are confirmed by straight numerical calculations. Second, Bogoliubov QPI of FeSexS1-x, where IBA provides a qualitative explanation for the particle-hole asymmetric Intensity in the calculation and experiments. 

[1] Hoffman et.al., Science 297, 1148 2002

[2] Wang and Lee, PRB 67, 020511, 2003

[3] Hirschfeld et.al., PRB 92, 184513 2015

[4] Capriotti et.al., PRB 68, 014508 2003

[5] Walker et al. arXiv:2306.01686 2023