Q-ball mechanism of electron transport properties of high-T$_c$ superconductors

TL;DR

This work develops a Euclidean Q-ball framework in which nested FS states generate finite-volume Q-balls formed by condensed SDW/CDW fluctuations that rotate in Matsubara time and carry a conserved Noether charge. Inside each Q-ball, nested fermions pair to form a superconducting condensate, lowering the energy and producing a pseudogap; the theory yields a first-order onset at $T^*$ for Q-ball formation and a second-order superconducting transition with a phase diagram featuring a dome that intersects the strange-metal region. Transport emerges from electron scattering off Q-ball fluctuations, generating a Planckian, linear-$T$ resistivity, while the large-Q-ball regime leads to hydrodynamic CDW sliding with a distinct scaling of conductivity and a diamagnetic response consistent with experiments. The framework links short-range SDW/CDW fluctuations, pseudogap physics, and strange-metal transport in cuprates, and its predictions align with micro X-ray diffraction data and observed diamagnetism. Overall, the Q-ball mechanism provides a cohesive picture of the pseudogap and strange-metal phenomena in high-$T_c$ cuprates and suggests new avenues to probe thermodynamic quantum time-crystal fluctuations.

Abstract

A theory is presented of a mechanism of high-Tc superconductivity in cuprates, based on the fact that 'nested' fermionic states near the Fermi surface of electrons/holes cause instability with respect to formation of the Q-balls (nontopological solitons) of coherently condensed spin/charge density wave fluctuations (SDW/CDW) with the wave-vector that matches the 'nesting' one. Simultaneously, the 'nested' fermions form superconducting condensate of Cooper/local pairs inside the Q-balls, with Q-ball SDW/CDW field being a 'pairing glue'. Thus, Q-balls possess lower total energy with respect to not condensed thermal SDW/CDW fluctuations and form a Q-balls 'gas' via first order phase transition below a temperature T$^*$. Besides, superconducting condensates inside the Q-balls induce a spectral gap on the nested parts of the Fermi surface, thus creating pseudogap phase. The Q-ball semiclassical field breaks chiral symmetry along the Matsubara time axis in Euclidean space-time possessing conserved Noether "charge" Q that makes the Q-ball volume finite. Prediction of the Q-ball scenario in cuprates is supported by micro X-ray diffraction data in HgBa$_2$CuO$_{4+y}$ in the pseudogap phase. The Q-balls of baryonic fields were originally predicted in Minkowski space-time by Sidney Coleman. In this paper it is demonstrated analytically that scattering of itinerant fermions on the Q-balls causes linear temperature dependence of electrical resistivity, that may explain famous 'Plankian' behavior in the 'strange metal' phase of high-Tc cuprates. Calculated diamagnetic response of Q-balls gas in the 'strange metal' phase and the phase diagram of high-Tc cuprates, with superconducting dome touching the 'strange metal' area at the optimal (holes)doping, are also in qualitative accord with experimental data.

Figures (5)

• Figure 1: The plots of $U_{eff}(M)$ at different normalised temperatures $T/T^*$ manifesting characteristic Q-ball local energy minimum at finite amplitude due to condensation of local/Cooper pairs inside Q-balls, obtained from Equations (\ref{['UFO1']}) and (\ref{['UFOI']}), see text.
• Figure 2: The contour plots of self-consistency equation (\ref{['self1']}) in the plane $\{M/\Omega;\, T=\Omega/2\pi\}$ are presented for 'mass' $\mu_0=0.157$ and different values of coupling constant $\kappa\equiv c4g\nu \varepsilon_0/3$, in arbitrary units, see text.
• Figure 3: The phase diagram that follows from Eq. (\ref{['self2']}), where $\kappa\equiv c \dfrac{4g\nu \varepsilon_0}{3}$, see text.
• Figure 4: The Dyson's equation for a fermion scattering by Q-balls of CDW/SDW bosonic field : the dashed line is CDW/SDW Q-ball bosonic Euclidean field correlator $D_M$ averaged over coordinates of Q-ball's centres in a crystal and Matsubara time zero-origin $\tau_0$. Heavy and thin lines are fermionic temperature Green's functions $G({r}-{r}')$ and $G_0({r}-{r}')$ respectively. Dots are vertices of fermion- Q-ball field $M$ interaction Eq. (\ref{['intinst0']}).
• Figure 5: Density of diamagnetic moment of the Q-balls gas in the PG phase $T_{1}^*(\kappa)<T<\mu_0/(2\pi )$, curves 1-3 correspond to different values of departure of the temperature $T$ from $T_{0}^*=\mu_0/(2\pi )$: $\mu_0/(2\pi )-T$ indicated in arb. units, see Fig. \ref{['triple']} and Eqs. (\ref{['Mstar']}), (\ref{['M1']}), (\ref{['M2']}).