  While in XX century the theory of superconductivity has focused on a
homogeneous metal with a rigid lattice which can be reduced to a single
effective conduction band in the dirty limit. Today in the XXI century, the
physics of superconductivity is focusing on complexity of quantum matter where
novel quantum functionalities with lattice inhomogeneity at nanoscale (between
1 nm and 100 nm) and at mesoscopic scale (in the range 100-10000 nm), where the
electronic structure need to be described by multiple Fermi surfaces and
multiple gaps in the superconducting phase in the clean limit. The present
issue of Journal of superconductivity and Novel magnetism collects papers
presented at the International Conference Superstripes 2019 which was held on
June 23-29, 2019, in Ischia Island, Italy. The series of Stripes conference
started on Dec 8 1996 and it has contributed to scientific advances in the new
physics of superconductivity in quantum complex systems in these last 23 years
where polarons, strain, multigap superconductivity, exchange interaction
between condensates, granular superconductivity and percolation play a key
role. The articles collected in this issue cover hot topics of the new quantum
physics of complex matter including the mechanism of high temperature
superconductivity, complex magnetic orders and orbital physics in strongly
correlated materials which have been growing rapidly in these last two years
opening new perspectives also in mesoscopic quantum engineering.
