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Physical review. B, Condensed matter

Theory of photoemission in the Hubbard model for Bi2 Sr2 CaCu2 O8

T. Dahm, Dirk Manske, Ludwig Tewordt

Published Jul 1, 1996• 5 citations
Publisher

Abstract

The quasiparticle spectral function is calculated for the 2D Hubbard model of Bi2212 with n\ensuremath{\sim}0.9. For momenta k\ensuremath{\gtrsim}${\mathit{k}}_{\mathit{F}}$ we obtain dips and satellite peaks at energies \ensuremath{\omega}0 which are caused by strong scattering of quasiparticles on antiferromagnetic spin fluctuations. These structures, which may be observable, become very pronounced below ${\mathit{T}}_{\mathit{c}}$ even for momenta k lying along the node of the ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$ wave gap. For k along the antinode of the gap we obtain below ${\mathit{T}}_{\mathit{c}}$ a shift of the quasiparticle peak and a dip in qualitative agreement with ARPES measurements on Bi2212. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.602

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The quasiparticle spectral function is calculated for the 2D Hubbard model of Bi2212 with n\ensuremath{\sim}0.9. For momenta k\ensuremath{\gtrsim}kF{\mathit{k}}_{\mathit{F}}kF​ we obtain dips and satellite peaks at energies \ensuremath{\omega}0 which are caused by strong scattering of quasiparticles on antiferromagnetic spin fluctuations. These structures, which may be observable, become very pronounced below Tc{\mathit{T}}_{\mathit{c}}Tc​ even for momenta k lying along the node of the dx2\ensuremath−y2{\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}dx2\ensuremath−y2​ wave gap. For k along the antinode of the gap we obtain below Tc{\mathit{T}}_{\mathit{c}}Tc​ a shift of the quasiparticle peak and a dip in qualitative agreement with ARPES measurements on Bi2212. \textcopyright{} 1996 The American Physical Society.
We have calculated within the fluctuation exchange approximation the full momentum and real-frequency dependence of the quasiparticle self-energy, the gap function, and the dynamic spin susceptibility for the two-dimensional Hubbard model near half filling. The spin-density-wave (SDW) instability is reached only asymptotically in the limit of infinite U or zero temperature. Near the SDW instability we find approximately marginal Fermi-liquid behavior, a pseudogap in the density of states, and a singlet dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2 pairing instability. Below Tc{\mathit{T}}_{\mathit{c}}Tc​, gaps open rapidly in the frequency spectra of the gap function, the quasiparticle scattering rate, and the density of states. The spectral density of the dynamic spin susceptibility agrees qualitatively with the neutron-scattering data on ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4{\mathrm{CuO}}_{4}CuO4​. The quasiparticle scattering rate and spin-lattice relaxation rate ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ decrease rapidly below Tc{\mathit{T}}_{\mathit{c}}Tc​. The photoemission intensities along the antinode and node of the gap are in good agreement with the angle-resolved photoemission spectroscopy data on Bi 2212. Including next-nearest-neighbor hopping we obtain for sufficiently large coupling (U/t\ensuremath{\gtrsim}7) a broad commensurate neutron-scattering peak like the observed one in YBa2{\mathrm{YBa}}_{2}YBa2​Cu3{\mathrm{Cu}}_{3}Cu3​O6+x{\mathrm{O}}_{6+\mathit{x}}O6+x​.
Abstract Using the strong-coupling diagram technique, low-temperature spectral properties of the two-dimensional fermionic Hubbard model are considered for strong and moderate Hubbard repulsions U . The electron hopping to the nearest, second and third neighbors is taken into account with hopping constants t , t ′ = − 0.3 t and t ″ = 0.2 t , respectively. The nonzero values of t ′ and t ″ lead to strong asymmetry in magnetic properties with respect to the hole and electron doping—for U = 8 t strong antiferromagnetic correlations are retained up to the electron concentration n ¯ ≈ 1.25 , while they are destroyed completely at n ¯ ≈ 0.87 . When the temperature is decreased to T ≲ 0.1 t , in a wide range of electron concentrations there appear narrow and intensive peaks at the Fermi level (FL) in densities of states. For U ≲ 6 t the peaks are seen even at half-filling, while for larger U they arise as the FL leaves the Mott gap. The peaks are connected with a narrow band emerging at low temperatures. We identify states forming the band with spin-polaron excitations—bound states of correlated electrons and mobile spin excitations. Obtained low-temperature spectral functions are used for interpreting the peak-dip-hump structure observed in the photoemission of Nd 2− x Ce x CuO 4 . In the case of hole doping, the calculated Fermi contour contains arcs near nodal points with pseudogaps near antinodal points, while for electron doping the spectral intensity is suppressed at hot spots, in agreement with experimental observations in cuprate perovskites.
The spectral weight A(p,\ensuremath{\omega}) of the two-dimensional t-J and Hubbard models has been calculated using exact diagonalization and quantum Monte Carlo techniques, at several densities 0.5\ensuremath{\le}〈n〉\ensuremath{\le}1.0. The photoemission (\ensuremath{\omega}0) region contains two dominant distinct features, namely a low-energy quasiparticle peak with bandwidth of order J, and a broad valence band peak at energies of order t. This behavior persists away from half-filling, as long as the antiferromagnetic correlations are robust. The results give support to theories of the copper oxide materials based on the behavior of holes in antiferromagnets, and they also provide theoretical guidance for the interpretation of experimental photoemission data for the cuprates.
Quantum Monte Carlo (QMC) and maximum-entropy techniques are used to study the spectral function $A(\mathbf{p},\ensuremath{\omega})$ of the one-band Hubbard model with strong coupling including a next-nearest-neighbor electronic hopping with amplitude ${t}^{\ensuremath{'}}/t=\ensuremath{-}0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for Sr2CuO2Cl2{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}Sr2​CuO2​Cl2​. A narrow quasiparticle (qp) band is observed in the QMC analysis at the temperature of the simulation T=t/3T=t/3T=t/3, both at and away from half-filling. Such a narrow band produces a large accumulation of weight in the density of states at the top of the valence band. As the electronic density 〈n〉〈n〉〈n〉 decreases further away from half-filling, the chemical potential travels through this energy window with a large number of states, and by $〈n〉\ensuremath{\sim}0.70$ it has crossed it entirely. The region near momentum $(0,\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ in the spectral function is more sensitive to doping than momenta along the diagonal from (0,0)(0,0)(0,0) to $(\ensuremath{\pi},\ensuremath{\pi})$. The evolution with hole density of the quasiparticle dispersion contains some of the features observed in recent ARPES data in the underdoped regime. For sufficiently large hole densities the ``flat'' bands at $(\ensuremath{\pi},0)$ cross the Fermi energy, a prediction that could be tested with ARPES techniques applied to overdoped cuprates. The population of the qp band introduces a hidden density in the system which produces interesting consequences when the quasiparticles are assumed to interact through antiferromagnetic fluctuations and studied with the BCS gap-equation formalism. In particular, a region of extended sss-wave character is found to compete with the ddd wave in the overdoped regime, i.e., when the chemical potential has almost entirely crossed the qp band as 〈n〉〈n〉〈n〉 is reduced. The present study also shows that previous ``real-space'' pairing theories for the cuprates, such as the antiferromagnetic Van Hove scenario, originally constructed based on information gathered at half-filling, do not change their predictions if hole dispersions resembling noninteracting electrons with renormalized parameters are used.
The momentum dispersion of the peak structure of the single-particle spectral weight A(p,\ensuremath{\omega}) of the two-dimensional Hubbard model is discussed. Using results obtained from Monte Carlo simulations on lattices up to 12\ifmmode\times\else\texttimes\fi{}12 in size, we determine the low-lying quasiparticle dispersion relation. This dispersion relation is anomalously flat near the (\ensuremath{\pi},0) and (0,\ensuremath{\pi}) points of the Brillouin zone, similar to the results of recent angular resolved photoemission measurements of the hole-doped cuprates. We argue that the generic nature of the quasiparticle dispersion relation observed in these materials arises from the strong Coulomb interaction and reflects the hole-spin correlations rather than the one-electron interactions which customarily determine the band structure.
We consider a two-dimensional Fermi liquid in the vicinity of a spin-density-wave transition to a phase with commensurate antiferromagnetic long-range order. We assume that near the transition, the Fermi surface is large and crosses the magnetic Brillouin zone boundary. We show that under these conditions, the self-energy corrections to the dynamical spin susceptibility, \ensuremath{\chi}(q,\ensuremath{\omega}), and to the quasiparticle spectral function, A(k,\ensuremath{\omega}), are divergent near the transition. We identify and sum the series of most singular diagrams, and obtain a solution for \ensuremath{\chi}(q,\ensuremath{\omega}) and an approximate solution for A(k,\ensuremath{\omega}). We show that (i) A(k) at a given, small \ensuremath{\omega} has an extra peak at k=kF{\mathit{k}}_{\mathit{F}}kF​+\ensuremath{\pi} (shadow band), and (ii) the dispersion near the crossing points is much flatter than for free electrons. The relevance of these results to recent photoemission experiments in YBa2{\mathrm{YBa}}_{2}YBa2​Cu3{\mathrm{Cu}}_{3}Cu3​${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ and Bi2{\mathrm{Bi}}_{2}Bi2​Sr2{\mathrm{Sr}}_{2}Sr2​CaCu2{\mathrm{CaCu}}_{2}CaCu2​O8{\mathrm{O}}_{8}O8​ systems is discussed.