  Solids with competing interactions often undergo complex phase transitions
with a variety of long-periodic modulations. Among such transition, devil's
staircase is the most complex phenomenon, and for it, CeSb is the most famous
material, where a number of the distinct phases with long-periodic
magnetostructures sequentially appear below the Neel temperature. An evolution
of the low-energy electronic structure going through the devil's staircase is
of special interest, which has, however, been elusive so far despite the
40-years of intense researches. Here we use bulk-sensitive angle-resolved
photoemission spectroscopy and reveal the devil's staircase transition of the
electronic structures. The magnetic reconstruction dramatically alters the band
dispersions at each transition. We moreover find that the well-defined band
picture largely collapses around the Fermi energy under the long-periodic
modulation of the transitional phase, while it recovers at the transition into
the lowest-temperature ground state. Our data provide the first direct evidence
for a significant reorganization of the electronic structures and spectral
functions occurring during the devil's staircase.
