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Nuclear Science and Techniques

Angle-resolved photoemission spectra in one-dimensional Hubbard-Holstein model

Sun Peijian, Ping Huai, Wei Zhang, Cheng Cheng, Zhu Zhi-yuan

Published Jan 1, 2011• 0 citations
Publisher

Abstract

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.

DOI
10.13538/j.1001-8042/nst.22.299-303

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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.
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.
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].
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.
We examine the single-particle excitation spectrum in the one-dimensional Hubbard-Holstein model at half-filling by performing a dynamical density matrix renormalization group calculation. The spin-charge separation is robust against the electron-phonon (EP) coupling, although both spinon and holon branches are affected by phonons. We find that this robustness is in sharp contrast to a rather strong influence of the EP coupling on quasiparticle properties in two dimensions. We discuss the implication of the results of recent angle-resolved photoemission spectroscopy measurements on SrCuO2\mathrm{Sr}\mathrm{Cu}{\mathrm{O}}_{2}SrCuO2​.
The Hubbard-Holstein model is one of the simplest to incorporate both electron-electron and electron-phonon interactions. In one dimension at half filling, the Holstein electron-phonon coupling promotes on-site pairs of electrons and a Peierls charge-density wave, while the Hubbard on-site Coulomb repulsion UUU promotes antiferromagnetic correlations and a Mott insulating state. Recent numerical studies have found a possible third intermediate phase between Peierls and Mott states. From direct calculations of charge and spin susceptibilities, we show that (i) as the electron-phonon coupling is increased, first a spin gap opens, followed by the Peierls transition. Between these two transitions, the metallic intermediate phase has a spin gap, no charge gap, and properties similar to the negative-UUU Hubbard model. (ii) The transitions between Mott/intermediate and intermediate/Peierls states are of the Kosterlitz-Thouless form. (iii) For larger UUU, the two transitions merge at a tricritical point into a single first-order Mott/Peierls transition. In addition, we show that an intermediate phase also occurs in the quarter-filled model.
We calculate the spectral function of the one-dimensional Hubbard-Holstein model using the time-dependent density matrix renormalization group, focusing on the regime of large local Coulomb repulsion, and away from electronic half-filling. We argue that, from weak to intermediate electron-phonon coupling, phonons interact only with the electronic charge, and not with the spin degrees of freedom. For strong electron-phonon interaction, spinon and holon bands are not discernible anymore and the system is well described by a spinless polaronic liquid. In this regime, we observe multiple peaks in the spectrum with an energy separation corresponding to the energy of the lattice vibrations (i.e., phonons). We support the numerical results by introducing a well controlled analytical approach based on Ogata-Shiba's factorized wave function, showing that the spectrum can be understood as a convolution of three contributions, originating from charge, spin, and lattice sectors. We recognize and interpret these signatures in the spectral properties and discuss the experimental implications.