Laser-induced nanocluster structures of different types (in topology and in elemental compositions of noble metal/carbon, bimetals, semiconductors, etc.) are studied theoretically and experimentally with allowance for the correlations in an ensemble of nanoparticles with quantum size states. The problem of high-temperature superconductivity (in the form of a sharp decrease in electrical resistivity) caused by topological surface structures leading to bound states of electrons based on new dimensional principles is discussed.