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arXiv:2304.10874

Bragg's law for X-ray scattering by quantum thermodynamic time crystals, Q-balls, as manifestation of the mechanism of High-T$_c$ superconductivity

Sergei I. Mukhin

Published Apr 21, 2023• 0 citations
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Abstract

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 HgBa$_2$CuO$_{4+y}$. 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-T$_c$ 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 $Ω=2πnT$ 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 HgBa$_2$CuO$_{4+y}$ reported recently. The T-linear dependence of electrical resistivity arises due to inverse temperature dependence of the Q-ball radius as function of temperature.

DOI
10.48550/arxiv.2304.10874

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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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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.
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.
Abstract The mysterious metallic phase showing T-linear resistivity and a universal scattering rate 1 / τ = α P k B T / ℏ with a universal prefactor α P ∼ 1 and logarithmic-in-temperature singular specific heat coefficient, the so-called ‘Planckian metal phase’ was observed in various overdoped high- T c cuprate superconductors over a finite range in doping. Revealing the mystery of the Planckian metal state is believed to be the key to understanding the mechanism for high- T c superconductivity. Here, we propose a generic microscopic mechanism for this state based on quantum-critical local bosonic charge Kondo fluctuations coupled to both spinon and a heavy conduction-electron Fermi surface within the heavy-fermion formulation of the slave-boson t–J model. By a controlled perturbative renormalization group analysis, we examine the competition between the pseudogap phase, characterized by Anderson’s Resonating-Valence-Bond spin-liquid, and the Fermi-liquid state, modeled by the electron hopping (effective charge Kondo effect). We find a quantum-critical metallic phase with a universal Planckian ℏ ω / k B T scaling in scattering rate near an extended localized-delocalized (pseudogap-to-Fermi liquid) charge-Kondo breakdown transition. The d-wave superconducting ground state emerges near the transition. Unprecedented qualitative and quantitative agreements are reached between our theoretical predictions and various experiments, including optical conductivity, universal doping-independent field-to-temperature scaling in magnetoresistance, specific heat coefficient, marginal Fermi-liquid spectral function observed in ARPES, and Fermi surface reconstruction observed in Hall coefficients in various overdoped cuprates. Our mechanism offers a microscopic understanding of the quantum-critical Planckian metal phase observed in cuprates and its link to the pseudogap, d-wave superconducting, and Fermi liquid phases. It offers a promising route for understanding how d-wave superconductivity emerges from such a strange metal phase in cuprates–one of the long-standing open problems in condensed matter physics since 1990s–as well as shows a broader implication for the Planckian strange metal states observed in other correlated unconventional superconductors.
The mysterious metallic phase showing perfect TTT-linear resistivity and a universal scattering rate 1/τ=αPkBT/ℏ1/τ= α_P k_B T /\hbar1/τ=αP​kB​T/ℏ with a universal prefactor αP∼1α_P \sim 1αP​∼1 and logarithmic-in-temperature singular specific heat coefficient, so-called Planckian metal phase was observed in various overdoped high-TcT_cTc​ cuprate superconductors over a finite range in doping. Here, we propose a microscopic mechanism for this exotic state based on quantum-critical bosonic charge Kondo fluctuations coupled to both spinon and a heavy conduction-electron Fermi surfaces within the heavy-fermion formulation of the slave-boson ttt-JJJ model. Using a controlled perturbative renormalization group (RG) analysis, we examine the competition between the pseudogap phase, characterized by Anderson's Resonating-Valence-Bond spin-liquid, and the Fermi-liquid state, characterized by the electron hoping (effective charge Kondo effect). We find a quantum-critical metallic phase with a universal Planckian ℏω/kBT\hbar ω/k_B Tℏω/kB​T scaling in scattering rate near a localized-delocalized (pseudogap-to-Fermi liquid) charge Kondo breakdown transition. Our results are in excellent agreement with the recent experimental observations on optical conductivity (without fine-tuning) in Nat. Commun. 14, 3033 (2023), universal doping-independent field-to-temperature scaling in magnetoresistance in Nature 595, 661 (2021), and the marginal Fermi-liquid spectral function observed in ARPES (Science 366, 1099 (2019)) as well as Hall coefficient in various overdoped cuprates in Nature 595, 661 (2021) and Annu. Rev. Condens. Matter Phys. 10, 409 (2019). Our mechanism offers a microscopic understanding of the quantum-critical Planckian metal phase observed in cuprates d-wave superconducting, and Fermi liquid phases.
Abstract. The normal state metallic behavior above the superconducting transition temperature (Tsc) remains one of the least understood properties since its discovery in cuprates by Bednorz and Müller [1]. Apart from the pseudogap (T ∗) phenomenon above Tsc, there is this T-linear resistivity that was first recognized by Anderson [2] as strange simply because it does not obey the low-temperature T 2 electron-electron scattering rate predicted from the Fermi liquid theory. Here, we prove that the finite temperature continu-ous quantum phase transition (CTQPT) is responsible for the transition from a strange metal to a Fermi liquid for a given chemical composition. Our proof follows the Green function formalism and the energy-level spacing renormal-ization group method. Interestingly, the CTQPT stated above can be related to the proof derived by Parameswaran, Shankar and Sondhi [3], in which, the one-to-one correspondence between the Fermi gas and Fermi liquid is indeed a special case. The theory is further exploited to give unambiguous explanations as to why and how doping gives rise to spectral weight transfer observed in the soft X-ray absorption spectroscopic measurements for the La-Sr-Cu-O system. PACS: 74.72.-h, 71.10.Hf, 74.25.F-, 74.25.Jb 1.
The mysterious quantum-critical Planckian bad metal phase with perfect T-linear resistivity persisting beyond the quasi-particle limit and universal T-linear scattering rate has been observed in various high-Tc cuprate superconductors. Here, we develop a realistic theoretical approach to this phase in an analytically solvable large-N multi-channel Kondo lattice model, derived from a heavy-fermion formulated conventionaL t-J model, known for qualitatively describing cuprates. This phase is originated from critical charge Kondo fluctuations where disordered local bosonic charge fluctuations couple to spinon and heavy conduction-electron Fermi surfaces near a charge-Kondo-breakdown local quantum critical point associated with pseudogap-to-Fermi liquid transition. Our results show excellent agreement with experiments and offer broad implications for other unconventional superconductors.
It is claimed by a recent quantum Monte Carlo simulation that the linear-in-temperature DC resistivity observed in the high-TcT_{c}Tc​ cuprate superconductors can be reproduced in the pure two dimensional Hubbard model\cite{Huang}. Here we show perturbatively that such a translational invariant electronic model can not support a steady state current in the presence of a uniform electric field at any finite temperature. Instead, the Hubbard model is perfectly conducting in the linear response regime and will undergo Bloch oscillation at finite electric field for any finite temperature. Nevertheless, the quantum Monte Carlo simulation can provide us the key information on the temperature dependence of the Drude weight, a quantity of central importance in the holographic description of the transport properties of the strange metal phase.