Euclidean Q-balls of electronic spin/charge densities confining superconducting condensates as the origin of pseudogap and high-Tc superconducting behaviours

Abstract

Euclidean Q-ball type solutions carrying Cooper/local-pair condensates inside finite volume filled with oscillating in Matsubara time semiclassical electronic spin/charge densities are found in the ‘nested’ repulsive Hubbard model of high-Tc superconductors. Euclidean Q-ball solutions, analogous to famous Q-balls of squarks in the supersymmetric standard model, arise due to global invariance of the effective theory under the phase rotation of the Fourier amplitudes of spin/charge density wave-like short-range fluctuations, leading to conservation of the ‘Noether charge’ Q along the Matsubara time axis. It is demonstrated analytically that condensation of Cooper/local pairs self-consistently creates local minimum at finite amplitude in the effective potential energy of the spin/charge density wave fluctuations. Exchange with density fluctuations of finite amplitude provides greater binding energy of fermions into local/Cooper pairs inside the Q-balls than exchange with infinitesimal lattice/charge/spin quasiparticles in the standard Fröhlich mechanism. The Q-balls arise with a finite density of superconducting condensate inside them below temperature T∗. Self-consistent solutions are found from the Eliashberg like equations with the ‘nesting’ wave vector of the spin-/charge fluctuations connecting ‘antinodal’ points of the Brillouin zone, combined with semiclassical equation for the minimum of Euclidean action of the fluctuations field. Fermionic spectral gap arises inside the Q-balls in the vicinity of the ‘antinodal’ points. The ‘breathing modes’ of the Q-balls in Matsubara time, as well as sharp maximum of specific heat across transition temperature T∗ into Q-balls gas phase are predicted.