Checkerboard local density of states in striped domains pinned by vortices

We discuss recent elastic neutron scattering and scanning tunneling experiments on high-$T_c$ cuprates exposed to an applied magnetic field. Antiferromagnetic vortex cores operating as pinning centers for surrounding stripes is qualitatively consistent with the neutron data provided the stripes have the antiphase modulation. Within a Green’s function formalism we study the low energy electronic structure around the vortices and find that besides the dispersive quantum interference there exists a non-dispersive checkerboard interference pattern consistent with recent scanning tunneling measurements. Thus both experiments can be explained from the physics of a single ${\mathrm{CuO}}_2$ plane.