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Path-integral theory for photoemission spectra of electron- phonon coupled systems and anomalous isotope effect

Kai Ji, Keiichirō Nasu

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

Using a new path-integral theory [1], we study the angle resolved photoemission spectra (ARPES) of one - and two-dimensional metallic many-electron systems coupled with Einstein phonons. The multiple scatterings of electrons due to phonons are shown to completely dominate the ARPES, even if the electron-phonon coupling strength is intermediate. These multiple scatterings result in spectral evolution from a broad Gaussian to a two-headed asymmetric Lorentzian as the momentum changes from the band bottom to the Fermi one ( ≡ pF ), as shown in Fig. 1. We have also found that this two-headed structure near pF becomes most distinct in the two dimensional non-half-filled cases with no charge density wave gap. These results qualitatively agree with recent experiments of ARPES on the Be(0001) surface and Bi2Sr2CaCu2O8. In terms of nonlinear couplings between the electrons and the phonons, we also show the microscopic origin of anomalous isotopic band shift appeared in the ARPES of Bi2Sr2CaCu2O8, in good agreement with the recently discovery by Gweon et al. [2].

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Using a new path-integral theory [1], we study the angle resolved photoemission spectra (ARPES) of one - and two-dimensional metallic many-electron systems coupled with Einstein phonons. The multiple scatterings of electrons due to phonons are shown to completely dominate the ARPES, even if the electron-phonon coupling strength is intermediate. These multiple scatterings result in spectral evolution from a broad Gaussian to a two-headed asymmetric Lorentzian as the momentum changes from the band bottom to the Fermi one ( ≡ pF ), as shown in Fig. 1. We have also found that this two-headed structure near pF becomes most distinct in the two dimensional non-half-filled cases with no charge density wave gap. These results qualitatively agree with recent experiments of ARPES on the Be(0001) surface and Bi2Sr2CaCu2O8. In terms of nonlinear couplings between the electrons and the phonons, we also show the microscopic origin of anomalous isotopic band shift appeared in the ARPES of Bi2Sr2CaCu2O8, in good agreement with the recently discovery by Gweon et al. [2].
The angle-resolved photoemission spectra (ARPES) of the spin-1/2 Holstein model at non-half-filling are calculated by using the adiabatic approximation and the classical Monte Carlo method. It is found that in the metallic state, the spectra take broad Gaussians at the band bottom, while evolving to sharp Lorentzians near the Fermi level, commonly in one, two, and three dimensions. We justify that this evolution in ARPES is connected with an electronic state transition from quasi-localized ones to the extended ones due to the scattering of electrons with the static lattice distortion.
In order to understand the effects of electron-phonon coupling and Coulomb interactions in angle-resolved photoemission spectroscopy (ARPES), a spin-1/2 Hubbard-Holstein model at half-filling is theoretically investigated by means of the mean field theory and classical Monte Carlo simulation method. It shows that the spectral shape of the one-dimensional system is significantly modified by the electron-phonon coupling and Coulomb interactions. The suppression of charge-density wave in one-dimensional system has been ascribed to the short-range Coulomb repulsion and thermal lattice fluctuations. The competition between these interactions can induce zero energy gaps in APPES as well as complete cancellation of charge or spin ordering.
We have developed a new approach, starting from the Frohlich Hamiltonian and by means of the unitary transformation with the perturbation treatment, to deal with the momentum-dependent spectral functions (MDSF) of electron-phonon coupling system. The approach takes care of the fact that only those electrons near the Fermi surface within a layer of width ${\ensuremath{\omega}}_{ph}$ (phonon frequency) are scattered by phonons strongly. Our results show that the MDSF is mainly composed of two parts: the zero-phonon part and the one-phonon one. When the bare electron energy ϵk{ϵ}_{\mathbf{k}}ϵk​ is close to the Fermi energy EF{E}_{F}EF​, $\ensuremath{\mid}{ϵ}_{\mathbf{k}}\ensuremath{-}{E}_{F}\ensuremath{\mid}\ensuremath{\simeq}{\ensuremath{\omega}}_{ph}$, the one-phonon part is quite significant and the MDSF shows a two-headed peak. However, for $\ensuremath{\mid}{ϵ}_{\mathbf{k}}\ensuremath{-}{E}_{F}\ensuremath{\mid}⪢{\ensuremath{\omega}}_{ph}$, the one-phonon part disappears gradually and the MDSF shows a single broad peak. Our calculation for MDSF is qualitatively in agreement with recent measurement of angle-resolved photoemission spectroscopy on the Be(0001) surface and Bi2Sr2CaCu2O8{\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8}Bi2​Sr2​CaCu2​O8​. Besides, the two-headed structure of MDSF indicates the ``hybridization'' between electrons and phonons.
We develop a novel self-consistent approach for studying the angle resolved photoemission spectra (ARPES) of a hole in the t-J Holstein model giving perfect agreement with numerically exact diagrammatic Monte Carlo (DMC) data at zero temperature for all regimes of electron-phonon coupling. Generalizing the approach to finite temperatures, we find that the anomalous temperature dependence of the ARPES in undoped cuprates is explained by cooperative interplay of coupling of the hole to magnetic fluctuations and strong electron-phonon interaction.
Very recently, the angle-resolved photoemission spectrum (ARPES) of [Ni(chxn)2Br]Br2[\mathrm{Ni}(\mathrm{chxn}{)}_{2}\mathrm{Br}]{\mathrm{Br}}_{2}[Ni(chxn)2​Br]Br2​ (chxn=1R,(\mathrm{chxn}=1R,(chxn=1R, 2R2R2R-cyclohexanediamine), which is a one-dimensional insulator driven by the strong Coulomb repulsion, has been experimentally observed. The experiment has clearly shown that a one-body gap appearing in the ARPES is much smaller than an optical gap observed in the light-absorption spectrum (LAS). The apparent difference between these two gaps indicates the breakdown of a mean-field description of this strongly correlated electron system. In this paper, we show that the ARPES and LAS of [Ni(chxn)2Br]Br2[\mathrm{Ni}(\mathrm{chxn}{)}_{2}\mathrm{Br}]{\mathrm{Br}}_{2}[Ni(chxn)2​Br]Br2​ are consistently explained within the framework of the one-dimensional extended Hubbard model. Lehmann spectra of the one-body and light-absorption-type two-body Green functions are calculated by a quantum Monte Carlo method. Our numerical results reproduce the experimentally observed ARPES and LAS, confirming the small one-body gap and large optical gap. The apparent difference in the gap structures can be explained by a dynamical Zeeman field induced by quantum fluctuations.
Angle-resolved photoemission spectroscopy (ARPES) has revealed peculiar properties of mobile dopants in correlated antiferromagnets (AFMs). But, describing them theoretically, even in simplified toy models, remains a challenge. Here, we study ARPES spectra of a single mobile hole in the $t\ensuremath{-}J$ model. Recent progress in the microscopic description of mobile dopants allows us to use a geometric decoupling of spin and charge fluctuations at strong couplings, from which we conjecture a one-to-one relation of the one-dopant spectral function and the spectrum of a constituting spinon in the undoped parent AFM. We thoroughly test this hypothesis for a single hole doped into a two-dimensional Heisenberg AFM by comparing our semianalytical predictions to previous quantum Monte Carlo results and our large-scale time-dependent matrix product state calculations of the spectral function. Our conclusion is supported by a microscopic trial wave function describing spinon-chargon bound states, which captures the momentum and t/Jt/Jt/J dependence of the quasiparticle residue. From our conjecture we speculate that ARPES measurements in the pseudogap phase of cuprates may directly reveal the Dirac-fermion nature of the constituting spinons. Specifically, we demonstrate that our trial wave function provides a microscopic explanation for the sudden drop of spectral weight around the nodal point associated with the formation of Fermi arcs, assuming that additional frustration suppresses long-range AFM ordering. We benchmark our results by studying the crossover from two to one dimension, where spinons and chargons are confined and deconfined, respectively.