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arXiv:1001.0573 · Physical Review B

Theory of the time-resolved spectral function of high-temperature superconductors with bosonic modes

Jianmin Tao, Jian‐Xin Zhu

Published Jun 8, 2010• 8 citations
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Abstract

We develop a three-temperature model to simulate the time dependence of the electron and phonon temperatures in high-temperature superconductors displaying strong anisotropic electron-phonon coupling. This model not only takes the tight-binding band structure into account but also is valid in the superconducting state. Based on this model, we calculate the time-resolved spectral function via the double-time Green's functions. We find that the dip-hump structure evolves with the time delay. More interestingly, an unusual structure is obtained when the phonons are pumped directly. This finding may serve as a direct evidence for electron-vibration mode coupling.

DOI
10.1103/physrevb.81.224506

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We develop a three-temperature model to simulate the time dependence of the electron and phonon temperatures in high-temperature superconductors displaying strong anisotropic electron-phonon coupling. This model not only takes the tight-binding band structure into account but also is valid in the superconducting state. Based on this model, we calculate the time-resolved spectral function via the double-time Green's functions. We find that the dip-hump structure evolves with the time delay. More interestingly, an unusual structure is obtained when the phonons are pumped directly. This finding may serve as a direct evidence for electron-vibration mode coupling.
We have recently developed a three-temperature model to simulate the time evolution of the electron and phonon temperatures in high-temperature superconductors. This is the first model that is valid in the superconducting state. Based on this model, we calculated the time-resolved spectral function via the double-time Green's functions. Our calculations show that the theory not only reveals the familiar dip-hump structure in the normal state, but also a new signature of the electron-phonon coupling in the superconducting state. We further show that this signature can only be observed when the phonons are pumped directly. In this proceedeing, we provide detailed derivation of our theory.
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.
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]).
We investigate the dynamics of a phonon-mediated superconductor driven out of equilibrium. The electronic hopping amplitude is ramped down in time, resulting in an increased electronic density of states. The dynamics of the coupled electron-phonon model is investigated by solving Migdal-Eliashberg equations for the double-time Keldysh Green's functions. The increase of the density of states near the Fermi level leads to an enhancement of superconductivity when the system thermalizes to the new state at the same temperature. We provide a time- and momentum-resolved view on this thermalization process and show that it involves fast processes associated with single-particle scattering and much slower dynamics associated with the superconducting order parameter. The importance of electron-phonon coupling for the rapid enhancement and the efficient thermalization of superconductivity is demonstrated, and the results are compared to a BCS time-dependent mean-field approximation.
One of the challenges in many-body physics is determining the effects of phonons on strongly correlated electrons. The difficulty arises from strong correlations at differing energy scales -- for band metals, Migdal-Eliashberg theory accurately determines electron-phonon coupling effects due to the absence of vertex corrections -- but strongly correlated electrons require a more complex description and the standard Migdal-Eliashberg approach does not necessarily apply. In this work, we solve for the atomic limit Green's function of the Holstein-Hubbard model with both time-dependent electron-electron and electron-phonon couplings. We derive nonequilibrium spectral moment sum rules for the first four moments of the single-particle Green's function. We then analytically confirm that this Green's function exactly satisfies the zeroth, first, and second moment sum rules, and provide numerical evidence that the third spectral moment sum rule also holds. Finally we calculate the two-particle Green's function in the atomic limit. These two functions are required inputs to create a self-consistent strong-coupling expansion for the lattice Green's functions of the Hubbard-Holstein model.
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.