Many-Impurity Effects in Fourier Transform Scanning Tunneling Spectroscopy

TL;DR

This paper develops a theoretical framework for understanding how multiple impurities affect Fourier transform scanning tunneling spectroscopy (FTSTS), demonstrating that averaging over configurations improves signal quality and allows extraction of the mean-free-path.

Contribution

A systematic treatment of many-impurity effects in FTSTS using variance analysis and diagrammatic perturbation theory, extending beyond isolated impurity models.

Findings

Configuration averaging reduces noise in FTSTS data.

Mean-free-path can be extracted from FTSTS measurements.

Diagrammatic perturbation theory models many-impurity effects.

Abstract

Fourier transform scanning tunneling spectroscopy (FTSTS) is a useful technique for extracting details of the momentum-resolved electronic band structure from inhomogeneities in the local density of states due to disorder-related quasiparticle scattering. To a large extent, current understanding of FTSTS is based on models of Friedel oscillations near isolated impurities. Here, a framework for understanding many-impurity effects is developed based on a systematic treatment of the variance Delta rho^2(q,omega) of the Fourier transformed local density of states rho(q,\omega). One important consequence of this work is a demonstration that the poor signal-to-noise ratio inherent in rho(q,omega) due to randomness in impurity positions can be eliminated by configuration averaging Delta rho^2(q,omega). Furthermore, we develop a diagrammatic perturbation theory for Delta rho^2(q,omega) and show that an important bulk quantity, the mean-free-path, can be extracted from FTSTS experiments.