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

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