Observing periodic gap variations in cuprates

Central to the enigma of the cuprates is ubiquitous electronic inhomogeneity arising from a variety of electronic orders that coexist with superconductivity, the individual signatures of which have been impossible to disentangle despite four decades of intense research. This strong nanoscale inhomogeneity complicates interpretation of measurements both by probes which average over this inhomogeneity and those, like scanning tunneling microscopy (STM), which should be able to spatially resolve variations driven by both order and inhomogeneity. Here, we develop a novel technique that directly acknowledges this electronic inhomogeneity and extracts statistically significant features from scanning tunneling spectroscopic data. Applying our novel technique to single and bilayer Bi-based cuprates spanning a large doping range, we peer through local inhomogeneities and find that the gap breaks translational and rotational symmetries and varies periodically in a four-fold pattern. Our direct observation of a symmetry breaking gap in the single particle tunneling spectra adds strong credence to the pair density wave hypotheses supposed to exist in these materials. We also discuss various implications of our observations and, in particular, how they can explain the origin of the low energy checkerboard pattern.