Real-space post-processing correction of thermal drift and piezoelectric actuator nonlinearities in scanning tunneling microscope images

In the high-transition-temperature (high-Tc) superconductors the pseudogap phase becomes predominant when the density of doped holes is reduced1. Within this phase it has been unclear which electronic symmetries (if any) are broken, what the identity of any associated order parameter might be, and which microscopic electronic degrees of freedom are active. Here we report the determination of a quantitative order parameter representing intra-unit-cell nematicity: the breaking of rotational symmetry by the electronic structure within CuO2 unit cell. We analyze spectroscopic-imaging scanning tunneling microscope images of the intra-unit-cell states in underdoped Bi2Sr2CaCu2O8+{\delta} and, using two independent evaluation techniques, find evidence for electronic nematicity of the states close to the pseudogap energy. Moreover, we demonstrate directly that these phenomena arise from electronic differences at the two oxygen sites within each unit cell. If the characteristics of the pseudogap seen here and by other techniques all have the same microscopic origin, this phase involves weak magnetic states at the O sites that break 90o -rotational symmetry within every CuO2 unit cell.

We report the development of revolving scanning transmission electron microscopy--RevSTEM--a technique that enables characterization and removal of sample drift distortion from atomic resolution images without the need for a priori crystal structure information. To measure and correct the distortion, we acquire an image series while rotating the scan coordinate system between successive frames. Through theory and experiment, we show that the revolving image series captures the information necessary to analyze sample drift rate and direction. At atomic resolution, we quantify the image distortion using the projective standard deviation, a rapid, real-space method to directly measure lattice vector angles. By fitting these angles to a physical model, we show that the refined drift parameters provide the input needed to correct distortion across the series. We demonstrate that RevSTEM simultaneously removes the need for a priori structure information to correct distortion, leads to a dramatically improved signal-to-noise ratio, and enables picometer precision and accuracy regardless of drift rate.