  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.
