  Spin-orbit interaction established itself as a major role player for emergent
phenomena in modern condensed matter including a topological insulator, spin
liquid and spin-dependent transports. However, its function is rather limited
to adding topological nature to each phases of matter. We prove by our spinor
line graph theory that a very strong spin-orbit interaction realized in 5d
pyrochlore electronic systems generates multiply degenerate perfect flat bands.
Unlike any of the previous flat bands, the electrons living there localize in
real space by destructively interfering with each other in a spin selective
manner ruled by the SU(2) gauge field. These electrons avoid the Coulomb
interaction by self-organizing their localized wave functions. This gives rise
to the trimerized charge ordering hand in hand with a stiff spin chirality,
which may explain the recently found exotic low-temperature insulating phase of
CsW2O6.
