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Direct visualization of electronic-structure symmetry within each crystallineunit cell is a new technique for complex electronic matter research. Bystudying the Bragg peaks in Fourier transforms of electronic structure images,and particularly by resolving both the real and imaginary components of theBragg amplitudes, distinct types of intra-unit cell symmetry breaking can bestudied. However, establishing the precise symmetry point of each unit cell inreal space is crucial in defining the phase for such Bragg-peak Fourieranalysis. Exemplary of this challenge is the high temperature superconductorBi2Sr2CaCu2O8+d for which the surface Bi atom locations are observable, whileit is the invisible Cu atoms that define the relevant CuO2 unit-cell symmetrypoint. Here we demonstrate, by imaging with picometer precision the electronicimpurity states at individual Zn atoms substituted at Cu sites, that the phaseestablished using the Bi lattice produces a ~2% (2pi) error relative to theactual Cu lattice. Such a phase assignment error would not diminish reliabilityin the determination of intra-unit-cell rotational symmetry breaking at theCuO2 plane. Moreover, this type of impurity atom substitution at the relevantsymmetry site can be of general utility in phase determination for Bragg-peakFourier analysis of intra-unit-cell symmetry.

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