  The high-temperature superconductivity in copper oxides emerges when carriers
are doped into the parent Mott insulator. This well-established fact has,
however, eluded a microscopic explanation. Here we show that the missing link
is the self-energy pole in the energy-momentum space. Its continuous evolution
with doping directly connects the Mott insulator and high-temperature
superconductivity. We show this by numerically studying the extremely small
doping region close to the Mott insulating phase in a standard model for
cuprates, the two-dimensional Hubbard model. We first identify two relevant
self-energy structures in the Mott insulator; the pole generating the Mott gap
and a relatively broad peak generating the so-called waterfall structure, which
is another consequence of strong correlations present in the Mott insulator. We
next reveal that either the Mott-gap pole or the waterfall structure (the
feature at the energy closer to the Fermi level) directly transforms itself
into another self-energy pole at the same energy and momentum when the system
is doped with carriers. The anomalous self-energy yielding the
superconductivity is simultaneously born exactly at this energy-momentum point.
Thus created self-energy pole, interpreted as arising from a hidden fermionic
excitation, continuously evolves upon further doping and considerably enhances
the superconductivity. Above the critical temperature, the same self-energy
pole generates a pseudogap in the normal state. We thus elucidate a unified
Mott-physics mechanism, where the self-energy structure inherent to the Mott
insulator directly gives birth to both the high-temperature superconductivity
and pseudogap.
