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Modern Physics Letters B

Pairon spectral function for high-Tc cuprate superconductors

Anita Kumari, Radhika Chauhan, B. D. Indu

Published Apr 17, 2023• 0 citations
Publisher

Abstract

The pairon spectral function for the high-[Formula: see text] cuprate superconductor [Formula: see text] has been evaluated through renormalized pairon frequency, analogous to the frequency (energy) of excited pairons. The exercise has been carried out with the help of many-body quantum dynamical Green’s function theory via a model Hamiltonian that includes the effects of the electrons, phonons, impurities and anharmonic fields. The analysis of the obtained results reveals that renormalized pairon frequency progressively increases up to the critical temperature [Formula: see text] and afterwards, instead of dropping to zero, it decreases smoothly with increasing temperature, capturing the essence of the pseudogap in high-[Formula: see text] cuprates. A further analysis of temperature-dependent spectral function also establishes the presence of the pseudogap above [Formula: see text]. The spectral function displays a conscious behavior with the variation of electron–phonon coupling constant ([Formula: see text]).

DOI
10.1142/s0217984923500380

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The pairon spectral function for the high-[Formula: see text] cuprate superconductor [Formula: see text] has been evaluated through renormalized pairon frequency, analogous to the frequency (energy) of excited pairons. The exercise has been carried out with the help of many-body quantum dynamical Green’s function theory via a model Hamiltonian that includes the effects of the electrons, phonons, impurities and anharmonic fields. The analysis of the obtained results reveals that renormalized pairon frequency progressively increases up to the critical temperature [Formula: see text] and afterwards, instead of dropping to zero, it decreases smoothly with increasing temperature, capturing the essence of the pseudogap in high-[Formula: see text] cuprates. A further analysis of temperature-dependent spectral function also establishes the presence of the pseudogap above [Formula: see text]. The spectral function displays a conscious behavior with the variation of electron–phonon coupling constant ([Formula: see text]).
The renormalized mode frequencies are obtained with the help of quantum dynamical approach of many body phonon Green’s function technique via a general Hamiltonian (excluding BCS Hamiltonian) including the effects of phonons and electrons, anharmonicities and electron-phonon interactions. The numerical estimates have been carried out to study the renormalized mode frequency of high temperature cuprate superconductor (HTS) YBa2Cu3O7-δ using modified Born-Mayer-Huggins interaction potential (MBMHP) best applicable to study the dynamical properties of all HTS.
Based on our improved SU(2) slave-boson approach (Phys. Rev. B 64, 052501(2001)) to the t-J Hamiltonian, we report a scaling behavior of pseudogap with doping and the temperature and doping dependence of spectral functions. In addition we discuss the cause of hump and quasi-particle peak in the observed spectral functions of high Tc cuprates. It is demonstrated that the sharpening of the observed quasi-particle peak below Tc is attributed to the bose condensation of holon pair. From the computed ratios of pseudogap Δ0Δ_0Δ0​ to both the superconducting temperature Tc and the pseudogap temperature T∗T^*T∗ as a function of hole doping concentration x, we find that there exists a universal scaling of these ratios with doping, that is, the hyperbolic scaling behavior of the former, 2Δ0kBTc∼x−α\frac{2 Δ_0}{k_B T_c} \sim x^{-α}kB​Tc​2Δ0​​∼x−α with α∼2α\sim 2α∼2 and near doping independence of the latter, 2Δ0kBT∗≈4∼6\frac{2 Δ_0}{k_B T^*} \approx 4 \sim 6kB​T∗2Δ0​​≈4∼6 are found.
We review nonperturbative numerical calculations on dynamical properties of the two-dimensional Hubbard model and their relevance to various spectroscopic experiments on high-temperature superconducting cuprates. The unbiased nonperturbative theories have revealed the existence of a self-energy singularity in slightly doped Mott insulators, which is responsible for both the pseudogap formation and high-temperature superconductivity. The self-energy pole traces back to the Mott gap at zero doping, underscoring that Mott physics lies at the heart of both the pseudogap and high-temperature superconductivity. This mechanism of the pseudogap relies neither on competing order nor preformed pair while that of the high superconducting transition temperature does not necessitate a bosonic glue to mediate Cooper pairing. Instead, both mechanisms are linked to the singular self-energy inherent to the Mott insulator. The presence of the self-energy pole accounts for various spectroscopic anomalies reported so far in experiments, deforming the spectral structure in a manner beyond a simple mass renormalization. The low-energy electron dynamics, as computed with the self-energy pole, suggest the existence of a hidden fermionic excitation coupling to quasiparticles.
The crossover from weak to strong coupling for a three-dimensional continuum model of fermions interacting via an attractive contact potential is studied above the superconducting critical temperature Tc.{T}_{c}.Tc​. The pair-fluctuation propagator, the one-loop self-energy, and the spectral function are investigated in a systematic way from the superconducting fluctuation regime (weak coupling) to the bosonic regime (strong coupling). Analytic and numerical results are reported. In the strong-coupling regime, where the pair fluctuation propagator has bosonic character, two quite different peaks appear in the spectral function at a given wave vector, a broad one at negative frequencies and a narrow one at positive frequencies. The broad peak is asymmetric about its maximum, with its spectral weight decreasing by increasing coupling and temperature. In this regime, two crossover temperatures T1∗{T}_{1}^{*}T1∗​ (at which the two peaks in the spectral function merge in one peak) and T0∗{T}_{0}^{*}T0∗​ (at which the maximum of the lower peak crosses zero frequency) can be identified, with ${T}_{c}\ensuremath{\ll}{T}_{0}^{*}<{T}_{1}^{*}.$ By decreasing coupling, the two-peak structure evolves smoothly. In the weak-coupling regime, where the fluctuation propagator has diffusive Ginzburg-Landau character, the overall line shape of the spectral function is more symmetric and the two crossover temperatures approach Tc.{T}_{c}.Tc​. The analysis of the spectral function identifies specific features which allow one to distinguish by ARPES whether a system is in the weak- or strong-coupling regime. Connection of the results of our analysis with the phenomenology of cuprate superconductors is also attempted.
Using the versatile double time thermodynamic Green's function approach based on many body theory the renormalized frequencies, phonon energy line widths, shifts and phonon density of states (PDOS) are investigated via a newly formulated Hamiltonian (does not include BCS type Hamiltonian) that includes the effects of electron-phonon, anharmonicities and that of isotopic impurities. The automatic appearance of pairons, temperature, impurity and electron-phonon coupling of renormalized frequencies, widths, shifts and PDOS emerges as a characteristic feature of present theory. The numerical investigations on PDOS for the YBa2Cu3O7 − δ crystal predicts several new feature of high temperature superconductors (HTS) and agreements with experimental observations.
We compute the finite-temperature single-particle spectral function of a one-dimensional Luttinger liquid coupled to an optical phonon band. The calculation is performed exactly for the case in which electron-phonon coupling is purely forward scattering. We extend the results to include backward scattering with a renormalization group treatment. The dispersion contains a change in velocity at the phonon energy, qualitatively similar to the case of electron-phonon coupling in a Fermi liquid. If the backward scattering part of the the electron-phonon interaction is not too strong compared to the forward scattering part, coupling to phonons also produces a pronounced peak in the spectral function at low energies. The calculated spectral function is remarkably similar to the angle-resolved photoemission spectra of the high-temperature superconductors, including the apparent presence of ``nodal quasiparticles,'' the presence of a ``kink'' in the dispersion, and the non-Fermi-liquid frequency and temperature dependencies. Although a microscopic justification has not been established for treating the electronic dynamics of the cuprates as quasi-one-dimensional, at the very least we take the quality of the comparison as evidence of the non-Fermi-liquid character of the measured spectra.