# Local and global patterns in quasiparticle interference: a reduced response function approach

## TL;DR

This paper introduces a reduced response function approach to analyze quasiparticle interference patterns, linking local and global features to electronic structure geometry, topology, and topological invariants in physical systems.

## Contribution

It develops a new RRF method for interpreting QPI patterns, connecting them to electronic topology and demonstrating robustness of topological indicators.

## Key findings

- Global QPI patterns can indicate topological numbers.
- The imaginary part of RRF is the generalized joint density of states.
- Robustness of topological indicators against local QPI features.

## Abstract

A physical system exposes to us in a real space, while its description often refers to its reciprocal momentum space. A connection between them can be established by exploring patterns of quasiparticles interference (QPI), which is experimentally accessible by Fourier transformation of the scanning tunneling spectroscopy (FT-STS). We here investigate how local and global features of QPI patterns are related to the geometry and topology of electronic structure in the considered physical system. A reduced response function (RRF) approach is developed that can analyze QPI patterns with clear physical pictures. It is justified that the generalized joint density of states, which is the imaginary part of RRF, for studying QPI. Moreover, we reveal that global patterns of QPI may be indicators of topological numbers for gapless systems, and demonstrate that robustness of such indicators against distractive local features of QPI for topological materials with complicated band structures.