Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0804.4196 · Physical Review B

Finite-temperature spectral function of a hole in a quantum antiferromagnet and the role of phonons

Satyaki Kar, Efstratios Manousakis

Published Aug 11, 2008• 9 citations
arXivHTMLPDF

Abstract

We study thermal broadening of the hole spectral function of the two-dimensional $t\text{\ensuremath{-}}J$ model (and its extensions) within the noncrossing approximation (NCA) with and without the contribution of optical phonons. We find that phonons at finite temperature broaden the lowest energy quasiparticle peak, however, the string excitations survive even for relatively strong electron-phonon coupling. Experimental angle-resolved photoemission spectroscopy (ARPES) results compare well with our calculations at finite temperature when we use strong electron-phonon coupling without any ad hoc broadening. In addition, we have studied the role of vertex corrections and we find that their contribution allows us to achieve the same overall agreement with the ARPES experimental results but using smaller values for the electron-phonon coupling $(\ensuremath{\gamma}\ensuremath{\sim}0.5)$ than that required $(\ensuremath{\gamma}\ensuremath{\sim}1)$ when restricting ourselves within NCA.

DOI
10.1103/physrevb.78.064508

Related papers

Electron-Phonon Coupling and a Polaron in the t−J Model: From the Weak to the Strong Coupling Regime

Andrei S. Mishchenko, Naoto Nagaosa

We present numeric results for ground state and angle resolved photoemission spectra (ARPES) for a single hole in the t-J model coupled to optical phonons. The systematic-error-free diagrammatic Monte Carlo method is employed where the Feynman graphs for the Matsubara Green function in imaginary time are summed up completely with respect to phonon variables, while magnetic variables are subjected to the noncrossing approximation. We obtain that at electron-phonon coupling constants relevant for high T(c) cuprates the polaron undergoes a self-trapping crossover to the strong-coupling limit and theoretical ARPES demonstrate features observed in experiment: A broad peak in the bottom of the spectra has momentum dependence which coincides with that of a hole in the pure t-J model.

arXiv:cond-mat/0403751•Physical Review Letters•Jul 12, 2004•208 citations

String excitations of a hole in a quantum antiferromagnet and photoelectron spectroscopy

Efstratios Manousakis

The aim of the present paper is twofold. The first goal is to show that high resolution angle-resolved photoelectron spectra from cuprates indicate the presence of string-like excitations of the quasihole excitation in a quantum antiferromagnet. In order to compare with the experimental intensity plots, we calculate the spectral function of the $t\ensuremath{-}J$ and the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}J$ models within the self-consistent Born approximation for widely accepted values of the parameters of these models. The main features of the high resolution photoelectron spectra are in general agreement with the results based on the above models and can be understood by considering not only the lowest-energy quasiparticle peak but, also, the higher-energy string-like excitations of the hole. These features are (a) the energy-momentum dispersion of the string-like excitations, (b) the momentum dependence of the spectral weight of the quasiparticle peak, and (c) the way in which the spectral weight of the lowest-energy quasiparticle peak is transferred to higher-energy string excitations, including the fact that it vanishes near the $\ensuremath{\Gamma}$ point. The second goal of the present paper is to make the case that a proper analysis of both the numerical results obtained from these models and of the experimental results, suggests a theoretical picture for the internal structure of the hole-quasiparticle and a string-exchange pairing mechanism due to strong antiferromagnetic correlations among the background spins. We find that, using a simple model in which the Hilbert space is restricted to states of only unbroken strings attached to the holes and in which the holes are connected with unbroken strings, we can provide a good quantitative description of the most accurate numerical results. We find that the holes experience an effective interaction due to a string-exchange mechanism which is characterized by a rather large string tension and this can provide pairing energy scales much larger than those suggested by spin-fluctuation-mediated pairing models. In addition, it is argued that such string-exchange interaction tends to bind holes in a bound state with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry.

arXiv:cond-mat/0702288•Physical Review B•Jan 8, 2007•79 citations

Spectral properties of a hole coupled to optical phonons in the generalized t−J model

J. Bonča, Sadamichi Maekawa, Takami Tohyama +1 more

We present an efficient numerical method for the description of ground state and spectral properties of a doped hole in generalized $t\text{\ensuremath{-}}J$ models coupled to optical phonons. In the weak-coupling regime, coherent hole motion is less affected by the electron-phonon (EP) interaction in the electron than in the hole-doped system. Increasing the strength of EP coupling leads to a vanishing low-energy spectral weight around $\ensuremath{\Gamma}$ point. Spectral properties are in the strong coupling regime consistent with recent high-resolution angle resolved photoemission spectra (ARPES) [K. M. Shen et al., Phys. Rev. Lett. 93, 267002 (2004)]. A waterfall-like feature appears connecting the dispersive low-energy band with the incoherent high-energy peak resembling ARPES data [F. Ronning et al., Phys. Rev. B 71, 094518 (2005)].

Physical Review B•Feb 28, 2008•36 citations

Spectral properties of thet-Jmodel in the presence of hole-phonon interaction

Bumsoo Kyung, Sergei I. Mukhin, Vladimir N. Kostur +1 more

We examine the effects of electron-phonon interaction on the dynamics of the charge carriers doped in two-dimensional (2D) Heisenberg antiferromagnet. The t-J model Hamiltonian with a Fr\"ohlich term which couples the holes to a dispersionless (optical) phonon mode is considered for low doping concentration. The evolution of the spectral density function, the density of states, and the momentum distribution function of the holes with an increase of the hole-phonon coupling constant g is studied numerically. As the coupling to a phonon mode increases the quasiparticle spectral weight decreases and a ``phonon satellite'' feature close to the quasiparticle peak becomes more pronounced. Furthermore, strong electron-phonon coupling smears the multimagnon resonances (``string states'') in the incoherent part of the spectral function. The jump in the momentum distribution function at the Fermi surface is reduced without changing the hole pocket volume, thereby providing a numerical verification of Luttinger theorem for this strongly interacting system. The vertex corrections due to electron-phonon interaction are negligible in spite of the fact that the ratio of the phonon frequency to the effective bandwidth is not small. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9609186•Physical review. B, Condensed matter•Nov 1, 1996•18 citations

Spectral function of a Luttinger liquid coupled to phonons and angle-resolved photoemission measurements in the cuprate superconductors

Ian P. Bindloss, Steven Allan Kivelson

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.

arXiv:cond-mat/0402457•Physical Review B•Jan 31, 2005•2 citations

Hole spectral functions in lightly doped quantum antiferromagnets

Satyaki Kar, Efstratios Manousakis

We study the hole and magnon spectral functions as a function of hole doping in the two-dimensional $t\ensuremath{-}J$ and $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ models working within the limits of spin-wave theory by linearizing the hole-spin-deviation interaction and by adapting the noncrossing approximation. We find that the staggered magnetization decreases rather rapidly with doping and it goes to zero at a few percent of hole concentration in both $t\ensuremath{-}J$ and $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ models. Furthermore, our results show that the residue of the quasiparticle peak at $\stackrel{P\vec}{G}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ decreases very rapidly with doping. We also find pockets centered at $\stackrel{P\vec}{G}$, (i) with an elliptical shape with large eccentricity along the antinodal direction in the case of the $t\ensuremath{-}J$ model and (ii) with an almost circular shape in the case of the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ model. Last, we show that the spectral intensity distribution in the doped antiferromagnet has a waterfall-like pattern along the nodal direction of the Brillouin zone, a feature that is also seen in angle-resolved photoemission spectroscopy measurements.

arXiv:1106.6332•Physical Review B•Nov 9, 2011•7 citations
We study thermal broadening of the hole spectral function of the two-dimensional t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model (and its extensions) within the noncrossing approximation (NCA) with and without the contribution of optical phonons. We find that phonons at finite temperature broaden the lowest energy quasiparticle peak, however, the string excitations survive even for relatively strong electron-phonon coupling. Experimental angle-resolved photoemission spectroscopy (ARPES) results compare well with our calculations at finite temperature when we use strong electron-phonon coupling without any ad hoc broadening. In addition, we have studied the role of vertex corrections and we find that their contribution allows us to achieve the same overall agreement with the ARPES experimental results but using smaller values for the electron-phonon coupling (\ensuremathγ\ensuremath∼0.5)(\ensuremath{\gamma}\ensuremath{\sim}0.5)(\ensuremathγ\ensuremath∼0.5) than that required (\ensuremathγ\ensuremath∼1)(\ensuremath{\gamma}\ensuremath{\sim}1)(\ensuremathγ\ensuremath∼1) when restricting ourselves within NCA.
We present numeric results for ground state and angle resolved photoemission spectra (ARPES) for a single hole in the t-J model coupled to optical phonons. The systematic-error-free diagrammatic Monte Carlo method is employed where the Feynman graphs for the Matsubara Green function in imaginary time are summed up completely with respect to phonon variables, while magnetic variables are subjected to the noncrossing approximation. We obtain that at electron-phonon coupling constants relevant for high T(c) cuprates the polaron undergoes a self-trapping crossover to the strong-coupling limit and theoretical ARPES demonstrate features observed in experiment: A broad peak in the bottom of the spectra has momentum dependence which coincides with that of a hole in the pure t-J model.
The aim of the present paper is twofold. The first goal is to show that high resolution angle-resolved photoelectron spectra from cuprates indicate the presence of string-like excitations of the quasihole excitation in a quantum antiferromagnet. In order to compare with the experimental intensity plots, we calculate the spectral function of the $t\ensuremath{-}J$ and the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}J$ models within the self-consistent Born approximation for widely accepted values of the parameters of these models. The main features of the high resolution photoelectron spectra are in general agreement with the results based on the above models and can be understood by considering not only the lowest-energy quasiparticle peak but, also, the higher-energy string-like excitations of the hole. These features are (a) the energy-momentum dispersion of the string-like excitations, (b) the momentum dependence of the spectral weight of the quasiparticle peak, and (c) the way in which the spectral weight of the lowest-energy quasiparticle peak is transferred to higher-energy string excitations, including the fact that it vanishes near the $\ensuremath{\Gamma}$ point. The second goal of the present paper is to make the case that a proper analysis of both the numerical results obtained from these models and of the experimental results, suggests a theoretical picture for the internal structure of the hole-quasiparticle and a string-exchange pairing mechanism due to strong antiferromagnetic correlations among the background spins. We find that, using a simple model in which the Hilbert space is restricted to states of only unbroken strings attached to the holes and in which the holes are connected with unbroken strings, we can provide a good quantitative description of the most accurate numerical results. We find that the holes experience an effective interaction due to a string-exchange mechanism which is characterized by a rather large string tension and this can provide pairing energy scales much larger than those suggested by spin-fluctuation-mediated pairing models. In addition, it is argued that such string-exchange interaction tends to bind holes in a bound state with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry.
We present an efficient numerical method for the description of ground state and spectral properties of a doped hole in generalized $t\text{\ensuremath{-}}J$ models coupled to optical phonons. In the weak-coupling regime, coherent hole motion is less affected by the electron-phonon (EP) interaction in the electron than in the hole-doped system. Increasing the strength of EP coupling leads to a vanishing low-energy spectral weight around $\ensuremath{\Gamma}$ point. Spectral properties are in the strong coupling regime consistent with recent high-resolution angle resolved photoemission spectra (ARPES) [K. M. Shen et al., Phys. Rev. Lett. 93, 267002 (2004)]. A waterfall-like feature appears connecting the dispersive low-energy band with the incoherent high-energy peak resembling ARPES data [F. Ronning et al., Phys. Rev. B 71, 094518 (2005)].
We examine the effects of electron-phonon interaction on the dynamics of the charge carriers doped in two-dimensional (2D) Heisenberg antiferromagnet. The t-J model Hamiltonian with a Fr\"ohlich term which couples the holes to a dispersionless (optical) phonon mode is considered for low doping concentration. The evolution of the spectral density function, the density of states, and the momentum distribution function of the holes with an increase of the hole-phonon coupling constant g is studied numerically. As the coupling to a phonon mode increases the quasiparticle spectral weight decreases and a ``phonon satellite'' feature close to the quasiparticle peak becomes more pronounced. Furthermore, strong electron-phonon coupling smears the multimagnon resonances (``string states'') in the incoherent part of the spectral function. The jump in the momentum distribution function at the Fermi surface is reduced without changing the hole pocket volume, thereby providing a numerical verification of Luttinger theorem for this strongly interacting system. The vertex corrections due to electron-phonon interaction are negligible in spite of the fact that the ratio of the phonon frequency to the effective bandwidth is not small. \textcopyright{} 1996 The American Physical Society.
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.
We study the hole and magnon spectral functions as a function of hole doping in the two-dimensional $t\ensuremath{-}J$ and $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ models working within the limits of spin-wave theory by linearizing the hole-spin-deviation interaction and by adapting the noncrossing approximation. We find that the staggered magnetization decreases rather rapidly with doping and it goes to zero at a few percent of hole concentration in both $t\ensuremath{-}J$ and $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ models. Furthermore, our results show that the residue of the quasiparticle peak at $\stackrel{P\vec}{G}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ decreases very rapidly with doping. We also find pockets centered at $\stackrel{P\vec}{G}$, (i) with an elliptical shape with large eccentricity along the antinodal direction in the case of the $t\ensuremath{-}J$ model and (ii) with an almost circular shape in the case of the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ model. Last, we show that the spectral intensity distribution in the doped antiferromagnet has a waterfall-like pattern along the nodal direction of the Brillouin zone, a feature that is also seen in angle-resolved photoemission spectroscopy measurements.