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Euclidean Q-balls of fluctuating SDW/CDW in the 'nested' Hubbard model of high-T$_c$ superconductors as the origin of pseudogap and superconducting behavior

Sergei I. Mukhin

Published Aug 23, 2021• 0 citations
OpenAlex

Abstract

Euclidean Q-ball type solutions carrying Cooper/local-pair condensates inside finite volume with classically oscillating in Matsubara time spin-/charge densities (SDW/CDW) are found in the 'nested' repulsive Hubbard model of high-T$_c$ superconductors. An exchange between fermions with coherently oscillating SDW/CDW inside the Q-balls provides `pairing glue', that couples fermions into Cooper/local-pairs. Euclidean Q-ball solutions arise below some temperature $T^{*}$ due to global invariance of the effective theory under the phase rotation of the SDW/CDW fluctuations amplitudes, that conserves a 'Noether charge' Q along the Matsubara time axis. At $T^{*}$ the classical SDW/CDW fluctuations arise via 1$^{st}$ order phase transition, while superconducting condensate density inside Q-balls is zero at $T^{*}$ and possesses a steep maximum at $T<T^{*}$, causing a similar maximum in specific heat of the Q-balls 'gas'. Below $T^{*}$ the volume of the Q-balls is inversely proportional to the square of SDW/CDW fluctuation amplitude. The fermionic spectral gap inside Euclidean Q-balls arises in the vicinity of the 'nested' regions of the bare Fermi surface and scales with the square root of the superconducting density. All the described solutions are found analytically from the Eliashberg like equations for the two cases of 'nesting' wave vectors: a CDW wave vector $Q_{CDW}$, connecting regions near the Fermi surface with equal signs of the superconducting order parameter, or for a SDW wave vector $Q_{SDW}$, connecting regions with the opposite signs of the $d$-wave superconducting order parameter. Possible relation of the presented theory with thermodynamic time-crystals and different properties of superconductors is discussed.

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Euclidean Q-balls of fluctuating SDW/CDW in the 'nested' Hubbard model of high-Tc_cc​ superconductors as the origin of pseudogap and superconducting behavior
Euclidean Q-ball type solutions carrying Cooper/local-pair condensates inside finite volume with classically oscillating in Matsubara time spin-/charge densities (SDW/CDW) are found in the 'nested' repulsive Hubbard model of high-Tc_cc​ superconductors. An exchange between fermions with coherently oscillating SDW/CDW inside the Q-balls provides `pairing glue', that couples fermions into Cooper/local-pairs. Euclidean Q-ball solutions arise below some temperature T∗T^{*}T∗ due to global invariance of the effective theory under the phase rotation of the SDW/CDW fluctuations amplitudes, that conserves a 'Noether charge' Q along the Matsubara time axis. At T∗T^{*}T∗ the classical SDW/CDW fluctuations arise via 1st^{st}st order phase transition, while superconducting condensate density inside Q-balls is zero at T∗T^{*}T∗ and possesses a steep maximum at T<T∗T<T^{*}T<T∗, causing a similar maximum in specific heat of the Q-balls 'gas'. Below T∗T^{*}T∗ the volume of the Q-balls is inversely proportional to the square of SDW/CDW fluctuation amplitude. The fermionic spectral gap inside Euclidean Q-balls arises in the vicinity of the 'nested' regions of the bare Fermi surface and scales with the square root of the superconducting density. All the described solutions are found analytically from the Eliashberg like equations for the two cases of 'nesting' wave vectors: a CDW wave vector QCDWQ_{CDW}QCDW​, connecting regions near the Fermi surface with equal signs of the superconducting order parameter, or for a SDW wave vector QSDWQ_{SDW}QSDW​, connecting regions with the opposite signs of the ddd-wave superconducting order parameter. Possible relation of the presented theory with thermodynamic time-crystals and different properties of superconductors is discussed.
Bragg's law for X-ray scattering by quantum thermodynamic time crystals, Q-balls, as manifestation of the mechanism of High-Tc_cc​ superconductivity
Proposed by the author Q-ball mechanism of the pseudogap state and high-Tc superconductivity in cuprates was recently supported by micro X-ray diffraction data in HgBa2_22​CuO4+y_{4+y}4+y​. This provides a remarkable opportunity to investigate X-ray diffraction produced by the quantum thermodynamic time crystals, a direct embodiment of those are just the Euclidean Q-balls considered in the aforementioned theory. Simultaneously, it is also demonstrated that T-linear temperature dependence of electrical resistivity in the Q-ball phase arises due to scattering of electrons on the condensed charge/spin fluctuations inside the Q-balls. This gives a clue concerning possible mechanism of T-linear behaviour of electrical resistivity in the strange metal phase of high-Tc_cc​ cuprates. For this purpose the Green's functions of X-ray photons and fermions scattered by the Q-balls in the pseudogap phase of high-Tc superconductors are calculated using the Feynman diagrammatic technique. The Bragg's peaks intensity, provided by the imaginary part of the retarded photon Green's function, is calculated. In total, obtained results describe X-ray and electron scattering on the finite size Q-ball of CDW/SDW density, that oscillates with bosonic frequency Ω=2πnTΩ=2πnTΩ=2πnT in Matsubara time, i.e. the quantum thermodynamic time crystal. It is found, that theoretical results are in good correspondence with X-ray diffraction data in HgBa2_22​CuO4+y_{4+y}4+y​ reported recently. The T-linear dependence of electrical resistivity arises due to inverse temperature dependence of the Q-ball radius as function of temperature.
We consider a lattice version of the ``negative-U′′U''U′′ Hubbard model in three dimensions, to study the crossover from a superconducting phase transition (dominated by phase fluctuation) to a regime where the amplitude of the superconducting order parameter controls the critical temperature. Starting from a fermionic Hamiltonian, we give a microscopic derivation of the effective action in terms of the relevant physical fields: the modulus and phase of the superconducting order parameter. Furthermore, by employing to the resulting coarse--grained quantum XY\mathrm{XY}XY model the phase fluctuation algebra between number and phase operators (given by the Euclidean group E2),{E}_{2}),E2​), we map the ``phase-only'' action onto a solvable quantum spherical model. We establish the self--consistent theory (involving both fermionic and bosonic degrees of freedom), and calculate the superconducting phase coherence transition temperature Tc{T}_{c}Tc​ as a function of the coupling strength ∣U∣,|U|,∣U∣, exhibiting a maximum where the behavior crosses over from BCS to Bose-Einstein (BE) condensation. We examine a pseudogap in the normal state which emerges naturally as a precursor of superconductivity at the second characteristic temperature Tg{T}_{g}Tg​ due to a state with bound pairs but without long--range phase coherence. Furthermore, we demonstrate that the reduced gaps of the model $2{\ensuremath{\Delta}}_{0}{/k}_{B}{T}_{g}\ensuremath{\sim}4$ is almost independent on the pairing strength ∣U∣/t,|U|/t,∣U∣/t, whereas $2{\ensuremath{\Delta}}_{0}{/k}_{B}{T}_{c}$ increases with increasing ∣U∣|U|∣U∣---in striking analogy with the phenomenology of the high--temperature cuprate superconductors when interpreted in terms of the BCS-BC crossover scenario.
We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |∆|, where ∆ is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the |∆|2 shift predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by copper based high temperature superconductors. Based on spin and charge fractionalization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductivity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractionalization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as “nodal-antinodal dichotomy” at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such universal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs.
In the self-consistent approximation for the two-dimensional mean-field model we found an analytic solution for the ground state with a coexisting ddd-wave symmetric bond ordered pair density wave (PDW) and spin (SDW) or charge (CDW) density waves, as observed in some high-temperature superconductors. In particular, the solution gives the same periodicity for CDW and PDW, and a pseudogap in the Fermi-excitation spectrum.
Cuprate superconductors host ddd-wave superconductivity (SC), a pseudogap (PG) with Fermi arcs and a strange metal (SM) with incoherent excitations and temperature-linear resistivity. These regimes emerge from the same doped Mott system but are usually described separately. Here a relative-momentum-local (RML) theory is constructed, with the exact spin-singlet Cooper representation of antiferromagnetic superexchange in the ttt-JJJ model serving as a common thread. Pair correlations organize the low-energy behaviour of this Cooper channel into phase-coherent static SC, phase-incoherent quasi-static PG and phase-incoherent dynamic SM. A static RML prescription yields an exactly solvable PG Hamiltonian with nodal electron poles, antinodal gaps, resolution-broadened Fermi arcs and gapless charge-2e2e2e Cooper surfaces. A Cooper-surface Lifshitz transition generates logarithmic enhancements in the specific-heat coefficient and charge response without a spin singularity. The particle-particle continuum at finite centre-of-mass momentum produces Ohmic damping, while a dynamic RML prescription yields a one-loop self-energy with marginal-Fermi-liquid scaling. Spectral-weight transfer in the physical pair spectrum diagnoses the PG--SM crossover, whereas nonzero phase stiffness and global phase coherence identify SC. The RML theory relates single-particle, pair-sensitive and thermodynamic probes to three infrared organizations of one Cooper channel. A decisive experimental signature would be zero-energy Cooper-surface ridges in two-electron angle-resolved photoemission spectroscopy (2e-ARPES).
An interplay between the superconductivity and spin density wave (SDW) is studied from the perturbative point of view based on the two dimensional Hubbard model. It is shown that the d-pairing superconductivity is induced by spin fluctuations near the SDW boundary. The superconducting transition temperature ( T c ) is found to be remarkably suppressed by the renormalization through the electron self-energy, and to be sensitive to the band parameters due to nesting of the Fermi surface and the presence of the van Hove singularity as well as to the Fermi energy and the on-site interaction. As a consequence T c is enhanced by the next-nearest-neighbour hopping integral. The relation between the present result and experiments of high T c superconductors is discussed.