On the Origin of the Checkerboard Pattern in Scanning Tunneling Microscopy Maps of Underdoped Cuprate Superconductors

The checkerboard pattern in the differential conductance maps on underdoped cuprates appears when the STM is placed above the O-sites in the outermost CuO$_{\text{2}}$-plane. In this position the interference between tunneling paths through the apical ions above the neighboring Cu-sites leads to an asymmetric weighting of final states in the two antinodal regions of ${\boldsymbol{k}}$-space. The form of the asymmetry in the differential conductance spectra in the checkerboard pattern favors asymmetry in the localization length rather than a nematic displacement as the underlying origin.