Picometer Registration of Zinc Impurity States in Bi2Sr2CaCu2O8+d for Phase Determination in Intra-unit-cell Fourier Transform STM

TL;DR

This study uses picometer-precision imaging of impurity states in a high-temperature superconductor to accurately determine the phase of intra-unit-cell symmetry, improving the reliability of symmetry analysis in complex electronic materials.

Contribution

The paper introduces a method to precisely establish the phase point of the CuO2 unit cell using impurity states, reducing phase errors in intra-unit-cell symmetry studies.

Findings

Impurity imaging achieves picometer precision in phase determination.

Phase errors of about 2% can occur without impurity-based correction.

Impurity substitution at symmetry sites aids in accurate Fourier analysis.

Abstract

Direct visualization of electronic-structure symmetry within each crystalline unit cell is a new technique for complex electronic matter research. By studying the Bragg peaks in Fourier transforms of electronic structure images, and particularly by resolving both the real and imaginary components of the Bragg amplitudes, distinct types of intra-unit cell symmetry breaking can be studied. However, establishing the precise symmetry point of each unit cell in real space is crucial in defining the phase for such Bragg-peak Fourier analysis. Exemplary of this challenge is the high temperature superconductor Bi2Sr2CaCu2O8+d for which the surface Bi atom locations are observable, while it is the invisible Cu atoms that define the relevant CuO2 unit-cell symmetry point. Here we demonstrate, by imaging with picometer precision the electronic impurity states at individual Zn atoms substituted at Cu sites, that the phase established using the Bi lattice produces a ~2% (2pi) error relative to the actual Cu lattice. Such a phase assignment error would not diminish reliability in the determination of intra-unit-cell rotational symmetry breaking at the CuO2 plane. Moreover, this type of impurity atom substitution at the relevant symmetry site can be of general utility in phase determination for Bragg-peak Fourier analysis of intra-unit-cell symmetry.