Holographic Maps of Quasiparticle Interference

TL;DR

This paper introduces holographic maps that analyze the phases of Fourier-transformed STM images to reveal detailed electronic structures in strongly correlated materials, resolving longstanding puzzles in cuprate superconductors.

Contribution

The authors develop a method to factor out random phases in Fourier amplitudes, enabling new insights into quasiparticle interference and electronic states in materials.

Findings

Holographic maps extract phase information from STM data.

Application to cuprates explains wavevector dichotomy.

Reveals the role of $d$-wave Wannier functions in electronic structure.

Abstract

The analysis of Fourier-transformed scanning-tunneling-microscopy (STM) images with subatomic resolution is a common tool for studying properties of quasiparticle excitations in strongly correlated materials. While Fourier amplitudes are generally complex valued, earlier analysis mostly considered only their absolute values. Their complex phases were deemed random, and thus irrelevant, due to the unknown positions of impurities in the sample. Here we show how to factor out these random phases by analysing overlaps between Fourier amplitudes that differ by reciprocal lattice vectors. The resulting holographic maps provide important and previously-unknown information about the electronic structures of materials. When applied to superconducting cuprates, our method solves a long-standing puzzle of the dichotomy between equivalent wavevectors. We show that $d$-wave Wannier functions of the conduction band provide a natural explanation for experimental results that were interpreted as evidence for competing unconventional charge modulations. Our work opens a new pathway to identify the nature of electronic states in STM measurements.