arXiv:cond-mat/9505063 · Physical Review Letters

Theory for the Excitation Spectrum of High- Tc Superconductors: Quasiparticle Dispersion and Shadows of the Fermi Surface

Marcel Langer, Jörg Schmalian, Slawomir Janusz Grabowski, Karl H. Bennemann

Published Dec 11, 1995• 125 citations

Abstract

Using a new method for the solution of the fluctuation exchange approximation equations, which allows the determination of the self-energy ${\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})$ of the 2D one-band Hubbard model on the real frequency axis, we calculate the doping dependence of the quasiparticle excitations of high-${T}_{c}$ superconductors. We obtain new results for the shadows of the Fermi surface, their dependence on the deformation of the quasiparticle dispersion, an anomalous $\ensuremath{\omega}$ dependence of $\mathrm{Im}{\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})$, and a related violation of the Luttinger theorem. This sheds new light on the influence of short range magnetic order on the low energy excitations and its significance for photoemission experiments.

DOI: 10.1103/physrevlett.75.4508

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Strongly Correlated Fermi Liquid and the Normal State of High Tc Superconductors

Ziqiang Wang

International Journal of Modern Physics BMar 1, 199218 citations

Spectral properties of the two-dimensional Hubbard model

V. Zlatić, K. D. Schotte, Gudrun Schliecker

Physical review. B, Condensed matterAug 1, 199525 citations

Superconductivity in the two-dimensional Hubbard model

J. Beenen, David M. Edwards

arXiv:cond-mat/9503054Physical review. B, Condensed matterNov 1, 1995111 citations

Nonlocal Excitation Spectra in Two-Dimensional Doped Hubbard Model

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Anomalous low-doping phase of the Hubbard model

C. Gröber, R. Eder, Werner R. Hanke

arXiv:cond-mat/0001366Physical review. B, Condensed matterAug 15, 2000137 citations

Effects of spin fluctuations in the t-J model

Th. Obermeier, Thomas Pruschke, J. Keller

Jan 1, 19961 citation

arXiv:cond-mat/9505063 · Physical Review Letters

Theory for the Excitation Spectrum of High- Tc Superconductors: Quasiparticle Dispersion and Shadows of the Fermi Surface

Marcel Langer, Jörg Schmalian, Slawomir Janusz Grabowski, Karl H. Bennemann

Published Dec 11, 1995• 125 citations

arXiv HTML PDF

Abstract

Using a new method for the solution of the fluctuation exchange approximation equations, which allows the determination of the self-energy

{\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})

of the 2D one-band Hubbard model on the real frequency axis, we calculate the doping dependence of the quasiparticle excitations of high-

{T}_{c}

superconductors. We obtain new results for the shadows of the Fermi surface, their dependence on the deformation of the quasiparticle dispersion, an anomalous

\ensuremath{\omega}

dependence of

\mathrm{Im}{\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})

, and a related violation of the Luttinger theorem. This sheds new light on the influence of short range magnetic order on the low energy excitations and its significance for photoemission experiments.

DOI: 10.1103/physrevlett.75.4508

Related papers

Strongly Correlated Fermi Liquid and the Normal State of High Tc Superconductors

Ziqiang Wang

New insights into the strongly correlated Fermi liquid state of the SU(N) infinite-U Hubbard and t-J models are presented in connection to the metallic state of unbroken symmetry of the copper oxide planes. The nature of single particle and collective excitations is analyzed and the Landau Fermi Liquid parameters are derived. The one-particle spectral function in the Hubbard valence band is obtained with both Hubbard and Gutzwiller-like features. A simple interpretation of the large incoherent background is given in terms of a superposition of quasiparticles and a collective mode describing the propagation of a bare hole in a large U system. The spin exchange interactions produce very low lying collective modes describing the propagation of staggered spin chirality which soften at incommensurate wavevectors. The quasiparticles are strongly scattered by the low lying chirality fluctuations resulting in deviations from canonical Fermi liquid behavior at low energy scales. Of the same origin, the quasiparticle self energy is found to be strongly k-dependent. It leads to corrections to the dispersion and enhancement of the quasiparticle lifetime in the hole-like region of the interacting Fermi surface. The combined effects are sufficient to produce a sign change in the Hall coefficient evaluated for parameters relevant to the copper oxide planes. We show that these models also exhibit a zero temperature fluctuation driven transition from Fermi liquid to non Fermi liquid phase without the onset of magnetic ordering below a critical doping δc=1/4N, whereby providing a microscopic mechanism for the destruction of the Fermi liquid coherence by strong longitudinal gauge fluctuations which represent the effects of the infinite-U constraint.New insights into the strongly correlated Fermi liquid state of the SU(N) infinite-U Hubbard and t-J models are presented in connection to the metallic state of unbroken symmetry of the copper oxide planes. The nature of single particle and collective excitations is analyzed and the Landau Fermi Liquid parameters are derived. The one-particle spectral function in the Hubbard valence band is obtained with both Hubbard and Gutzwiller-like features. A simple interpretation of the large incoherent background is given in terms of a superposition of quasiparticles and a collective mode describing the propagation of a bare hole in a large U system. The spin exchange interactions produce very low lying collective modes describing the propagation of staggered spin chirality which soften at incommensurate wavevectors. The quasiparticles are strongly scattered by the low lying chirality fluctuations resulting in deviations from canonical Fermi liquid behavior at low energy scales. Of the same origin, the quasiparticle self energy is found to be strongly k-dependent. It leads to corrections to the dispersion and enhancement of the quasiparticle lifetime in the hole-like region of the interacting Fermi surface. The combined effects are sufficient to produce a sign change in the Hall coefficient evaluated for parameters relevant to the copper oxide planes. We show that these models also exhibit a zero temperature fluctuation driven transition from Fermi liquid to non Fermi liquid phase without the onset of magnetic ordering below a critical doping δc=1/4N, whereby providing a microscopic mechanism for the destruction of the Fermi liquid coherence by strong longitudinal gauge fluctuations which represent the effects of the infinite-U constraint.

International Journal of Modern Physics BMar 1, 199218 citations

Spectral properties of the two-dimensional Hubbard model

V. Zlatić, K. D. Schotte, Gudrun Schliecker

The self-energy of the hole-doped two-dimensional (2D) Hubbard model is calculated to second order in the interaction U and the ensuing renormalization of the spectral properties and of the Fermi surface is discussed. In uncorrelated systems the square-shaped Fermi surface separates the Fermi surface closed around the \ensuremath{\Gamma} point (with more holes than particles) from the Fermi surface closed around the Z point (with more particles than holes). In a correlated system a topological change from a Fermi surface centered around the \ensuremath{\Gamma} point to a Fermi surface closed around a Z point is induced, either by increasing the interaction or by diminishing the concentration of holes. The shape of the renormalized spectral function ${\mathit{A}}_{\mathbf{p}}$ (\ensuremath{\omega}) is momentum dependent. Using ${\mathit{A}}_{\mathbf{p}}$ (\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.The self-energy of the hole-doped two-dimensional (2D) Hubbard model is calculated to second order in the interaction U and the ensuing renormalization of the spectral properties and of the Fermi surface is discussed. In uncorrelated systems the square-shaped Fermi surface separates the Fermi surface closed around the \ensuremath{\Gamma} point (with more holes than particles) from the Fermi surface closed around the Z point (with more particles than holes). In a correlated system a topological change from a Fermi surface centered around the \ensuremath{\Gamma} point to a Fermi surface closed around a Z point is induced, either by increasing the interaction or by diminishing the concentration of holes. The shape of the renormalized spectral function ${\mathit{A}}_{\mathbf{p}}$(\ensuremath{\omega}) is momentum dependent. Using ${\mathit{A}}_{\mathbf{p}}$(\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.

Physical review. B, Condensed matterAug 1, 199525 citations

Superconductivity in the two-dimensional Hubbard model

J. Beenen, David M. Edwards

Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one-particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (\ensuremath{\pi},0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. A self-consistent solution with singlet ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is found and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest-neighbor antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favoring superconductivity. However, the mechanism for superconductivity is a local one, in contrast to spin-fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature ${\mathit{T}}_{\mathit{c}}$ is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/ ${\mathit{kT}}_{\mathit{c}}$ \ensuremath{\simeq}4.Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one-particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (\ensuremath{\pi},0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. A self-consistent solution with singlet ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is found and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest-neighbor antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favoring superconductivity. However, the mechanism for superconductivity is a local one, in contrast to spin-fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature ${\mathit{T}}_{\mathit{c}}$ is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/${\mathit{kT}}_{\mathit{c}}$\ensuremath{\simeq}4.

arXiv:cond-mat/9503054Physical review. B, Condensed matterNov 1, 1995111 citations

Nonlocal Excitation Spectra in Two-Dimensional Doped Hubbard Model

Yoshiro Kakehashi, Peter Fulde

Single-particle excitation spectra of the two-dimensional Hubbard model on the square lattice near half filling and at zero temperature are investigated on the basis of the self-consistent projection operator method. The method guarantees a high accuracy of the spectra with high energy and high momentum resolutions. It takes into account long-range intersite correlations as well as the strong on-site correlations. Effects of nonlocal excitations are clarified by comparing the results with those of the single-site approximation. The calculated spectra verify the quantum Monte-Carlo results for finite temperatures. The spectra at the Fermi level yield a hole-like Fermi surface in the underdoped region and an electron-like Fermi surface in the overdoped region. From a numerical analysis of the momentum dependent effective mass and self-energy, it is concluded that a marginal Fermi-liquid like state persists even at finite doping concentrations in the strongly correlated region because a van Hove singularity is pinned to the Fermi surface. It is also found that a kink structure appears in the quasiparticle energy band in the same region. The kink is shown to be caused by a mixing between the quasiparticle band and an excitation band with strong short-range antiferromagnetic correlations. These results suggest an explanation for some of the unusual properties of the normal state in high- $T_{\rm c}$ cuprates.Single-particle excitation spectra of the two-dimensional Hubbard model on the square lattice near half filling and at zero temperature are investigated on the basis of the self-consistent projection operator method. The method guarantees a high accuracy of the spectra with high energy and high momentum resolutions. It takes into account long-range intersite correlations as well as the strong on-site correlations. Effects of nonlocal excitations are clarified by comparing the results with those of the single-site approximation. The calculated spectra verify the quantum Monte-Carlo results for finite temperatures. The spectra at the Fermi level yield a hole-like Fermi surface in the underdoped region and an electron-like Fermi surface in the overdoped region. From a numerical analysis of the momentum dependent effective mass and self-energy, it is concluded that a marginal Fermi-liquid like state persists even at finite doping concentrations in the strongly correlated region because a van Hove singularity is pinned to the Fermi surface. It is also found that a kink structure appears in the quasiparticle energy band in the same region. The kink is shown to be caused by a mixing between the quasiparticle band and an excitation band with strong short-range antiferromagnetic correlations. These results suggest an explanation for some of the unusual properties of the normal state in high-$T_{\rm c}$ cuprates.

arXiv:0705.0581Journal of the Physical Society of JapanJun 25, 20074 citations

Anomalous low-doping phase of the Hubbard model

C. Gröber, R. Eder, Werner R. Hanke

We present results of a systematic quantum Monte Carlo study for the single-band Hubbard model. Thereby we evaluated single-particle spectra (PES and IPES), two-particle spectra (spin and density correlation functions), and the dynamical correlation function of suitably defined diagnostic operators, all as a function of temperature and hole doping. The results allow us to identify different physical regimes. Near half-filling we find an anomalous ``Hubbard-I phase,'' where the band structure is, up to some minor modifications, consistent with the Hubbard-I predictions. At lower temperatures, where the spin response becomes sharp, additional dispersionless ``bands'' emerge due to the dressing of electrons/holes with spin excitations. We present a simple phenomenological fit that reproduces the band structure of the insulator quantitatively. The Fermi surface volume in the low-doping phase, as derived from the single-particle spectral function, is not consistent with the Luttinger theorem, but qualitatively in agreement with the predictions of the Hubbard-I approximation. The anomalous phase extends up to a hole concentration of $\ensuremath{\approx}15%,$ i.e., the underdoped region in the phase diagram of high- ${T}_{c}$ superconductors. We also investigate the nature of the magnetic ordering transition in the single-particle spectra. We show that the transition to a spin-density wave-like band structure is not accomplished by the formation of any resolvable ``precursor bands,'' but rather by a (spectroscopically invisible) band of spin-3/2 quasiparticles. We discuss implications for the ``remnant Fermi surface'' in insulating cuprate compounds and the shadow bands in the doped materials.We present results of a systematic quantum Monte Carlo study for the single-band Hubbard model. Thereby we evaluated single-particle spectra (PES and IPES), two-particle spectra (spin and density correlation functions), and the dynamical correlation function of suitably defined diagnostic operators, all as a function of temperature and hole doping. The results allow us to identify different physical regimes. Near half-filling we find an anomalous ``Hubbard-I phase,'' where the band structure is, up to some minor modifications, consistent with the Hubbard-I predictions. At lower temperatures, where the spin response becomes sharp, additional dispersionless ``bands'' emerge due to the dressing of electrons/holes with spin excitations. We present a simple phenomenological fit that reproduces the band structure of the insulator quantitatively. The Fermi surface volume in the low-doping phase, as derived from the single-particle spectral function, is not consistent with the Luttinger theorem, but qualitatively in agreement with the predictions of the Hubbard-I approximation. The anomalous phase extends up to a hole concentration of $\ensuremath{\approx}15%,$ i.e., the underdoped region in the phase diagram of high-${T}_{c}$ superconductors. We also investigate the nature of the magnetic ordering transition in the single-particle spectra. We show that the transition to a spin-density wave-like band structure is not accomplished by the formation of any resolvable ``precursor bands,'' but rather by a (spectroscopically invisible) band of spin-3/2 quasiparticles. We discuss implications for the ``remnant Fermi surface'' in insulating cuprate compounds and the shadow bands in the doped materials.

arXiv:cond-mat/0001366Physical review. B, Condensed matterAug 15, 2000137 citations

Effects of spin fluctuations in the t-J model

Th. Obermeier, Thomas Pruschke, J. Keller

Recent experiments on the Fermi surface and the electronic structure of the cuprate-supercondutors showed the importance of short range antiferromagnetic correlations for the physics in these systems. Theoretically, features like shadow bands were predicted and calculated mainly for the Hubbard model. In our approach we calculate an approximate selfenergy of the t-J model. Solving the U = ∞ Hubbard model in the Dynamical Mean Field Theory (DMFT) yields a selfenergy that contains most of the local correlations as a starting point. Effects of the nearest neighbor spin interaction J are then included in a heuristical manner. Formally like in J-perturbation theory all ring diagrams, with the single bubble assumed to be purely local, are summed to get a correction to the DMFT-self engergy This procedure causes new bands and can furnish strong deformation of quasiparticle bands. The obvious importance of antiferromagnetic (AF) correlations for the physics of cuprate superconductors found an impressing confirmation through ARUPS-experiments performed by Aebi et al. [1]. There, in a Fermi surface (FS) mapping of Bi2Sr2CaCu2O8(001) shadows of the FS were observed. The interpretation as an effect of short range antiferromagnetic correlations led to an intensive discussion of so called shadow features, which have been predicted by Kampf and Schrieffer [2] in a semi-phenomenological theory for the Hubbard model. In the paper we present an approximate evaluation of the self energy for the t-J model HtJ consisting of two parts: The hopping term Ht = − t∗Recent experiments on the Fermi surface and the electronic structure of the cuprate-supercondutors showed the importance of short range antiferromagnetic correlations for the physics in these systems. Theoretically, features like shadow bands were predicted and calculated mainly for the Hubbard model. In our approach we calculate an approximate selfenergy of the t-J model. Solving the U = ∞ Hubbard model in the Dynamical Mean Field Theory (DMFT) yields a selfenergy that contains most of the local correlations as a starting point. Effects of the nearest neighbor spin interaction J are then included in a heuristical manner. Formally like in J-perturbation theory all ring diagrams, with the single bubble assumed to be purely local, are summed to get a correction to the DMFT-self engergy This procedure causes new bands and can furnish strong deformation of quasiparticle bands. The obvious importance of antiferromagnetic (AF) correlations for the physics of cuprate superconductors found an impressing confirmation through ARUPS-experiments performed by Aebi et al. [1]. There, in a Fermi surface (FS) mapping of Bi2Sr2CaCu2O8(001) shadows of the FS were observed. The interpretation as an effect of short range antiferromagnetic correlations led to an intensive discussion of so called shadow features, which have been predicted by Kampf and Schrieffer [2] in a semi-phenomenological theory for the Hubbard model. In the paper we present an approximate evaluation of the self energy for the t-J model HtJ consisting of two parts: The hopping term Ht = − t∗

Jan 1, 19961 citation

Using a new method for the solution of the fluctuation exchange approximation equations, which allows the determination of the self-energy

{\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})

of the 2D one-band Hubbard model on the real frequency axis, we calculate the doping dependence of the quasiparticle excitations of high-

{T}_{c}

superconductors. We obtain new results for the shadows of the Fermi surface, their dependence on the deformation of the quasiparticle dispersion, an anomalous

\ensuremath{\omega}

dependence of

\mathrm{Im}{\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})

{\mathit{A}}_{\mathbf{p}}

(\ensuremath{\omega}) is momentum dependent. Using

{\mathit{A}}_{\mathbf{p}}

(\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.

{\mathit{T}}_{\mathit{c}}

is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/

{\mathit{kT}}_{\mathit{c}}

\ensuremath{\simeq}4.

T_{\rm c}

cuprates.

{T}_{c}

superconductors. We also investigate the nature of the magnetic ordering transition in the single-particle spectra. We show that the transition to a spin-density wave-like band structure is not accomplished by the formation of any resolvable ``precursor bands,'' but rather by a (spectroscopically invisible) band of spin-3/2 quasiparticles. We discuss implications for the ``remnant Fermi surface'' in insulating cuprate compounds and the shadow bands in the doped materials.