  A magnetic field applied to type-II superconductors introduces quantized
vortices that locally quench superconductivity, providing a unique opportunity
to investigate electronic orders that may compete with superconductivity. This
is especially true in cuprate superconductors in which mutual relationships
among superconductivity, pseudogap, and broken-spatial-symmetry states have
attracted much attention. Here we observe energy and momentum dependent
bipartite electronic superstructures in the vortex core of
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ using spectroscopic-imaging scanning
tunneling microscopy (SI-STM). In the low-energy range where the nodal
Bogoliubov quasiparticles are well-defined, we show that the quasiparticle
scattering off vortices generates the electronic superstructure known as
"vortex checkerboard". In the high-energy region where the pseudogap develops,
vortices amplify the broken-spatial-symmetry patterns that preexist in zero
field. These data reveal canonical d-wave superconductivity near the node, yet
competition between superconductivity and broken-spatial-symmetry states near
the antinode.
