Q-ball mechanism of electron transport and spin/phonon excitations properties of high-T$_c$ superconductors

Abstract

Recently proposed by the author theory of the Q-balls mechanism of high-Tc superconductivity in cuprates is applied to explanation of known experimental data. The Q-balls (nontopological solitons) of coherently condensed spin/charge density wave fluctuations (SDW/CDW) with zero static mean and with the wave-vector that connects the 'nested' regions of the Fermi surface in doped cuprates cause pairing of the 'nested' fermions into local superconducting condensates. Hence, the Q-balls possess lower total energy in comparison with not condensed thermal SDW/CDW fluctuations in the same volume. Here it is demonstrated analytically that scattering of itinerant fermions on the Q-balls causes: linear temperature dependence of electrical resistivity in the interval of temperatures above T$_c$, reminiscent of the famous 'Plankian' behavior in the 'strange metal' phase; the famous hourglass dispersion close to forming Q-balls SDW fluctuations antiferromagnetic wave vectors and anomalous phonons dispersion softening close to CDW fluctuations wave vectors in the Brillouin zone. The diamagnetic response of Q-balls gas and contour plot of the Q-balls phase diagram, with lower temperatures dome touching the upper 'strange metal' one, are in qualitative accord with experimental data in high-T$_c$ cuprates. The superconducting condensates inside the Q-balls induce a spectral gap on the nested parts of the Fermi surface that might be responsible for a pseudogap phase in cuprates, where the Q-ball scenario was supported recently by micro X-ray diffraction data in HgBa$_2$CuO$_{4+y}$.