  While for many years the lattice, electronic and magnetic complexity of
high-temperature superconductors (HTS) has been considered responsible for
hindering the search of the mechanism of HTS now the complexity of HTS is
proposed to be essential for the quantum mechanism raising the superconducting
critical temperature. The complexity is shown by the lattice heterogeneous
architecture: a) heterostructures at atomic limit; b) electronic heterogeneity:
multiple components in the normal phase; c) superconducting heterogeneity:
multiple superconducting gaps in different points of the real space and of the
momentum space. The complex phase separation forms an unconventional granular
superconductor in a landscape of nanoscale superconducting striped droplets
which is called the "superstripes" scenario. The interplay and competition
between magnetic orbital charge and lattice fluctuations seems to be essential
for the quantum mechanism that suppresses thermal decoherence effects at an
optimum inhomogeneity.
