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arXiv:cond-mat/9702221 · Physical review. B, Condensed matter

Photoemission spectra of the t - J model in one and two dimensions: Similarities and differences

R. Eder, Y. Ohta

Published Aug 1, 1997• 25 citations
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Abstract

We present an exact diagonalization study of the single-particle spectral function in the one-dimensional (1D) and two-dimensional (2D) $t$-$J$ model. By studying the scaling properties with $J$ and $t$ we find a simple building pattern in 1D and show that every spectral feature can be uniquely assigned by a spinon and holon momentum. We find two types of low-energy excitations: A band with energy scale $J$ and high spectral weight disperses upwards in the interior part of the Brillouin zone and reaches ${E}_{F}$ at ${k}_{F},$ and a band with energy scale $t$ and low spectral weight disperses downwards in the outer part of the zone, touching ${E}_{F}$ at ${3k}_{F}.$ An analogous analysis of the 2D case at half-filling shows that the $t$ band exists also in this case, but is diffuse and never reaches the Fermi energy. For the doped case in 2D the picture is more reminiscent of 1D; in particular, the ``main band'' with a dispersion $\ensuremath{\propto}J$ and the ``shadow band'' with energy scale $t$ can be identified also in this case. This leads us to propose that the shadow bands discovered by Aebi et al. in Bi2212 are the 2D analog of the ${3k}_{F}$ singularity in 1D systems and unrelated to antiferromagnetic spin fluctuations.

DOI
10.1103/physrevb.56.2542

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We present an exact diagonalization study of the single-particle spectral function in the one-dimensional (1D) and two-dimensional (2D) ttt-JJJ model. By studying the scaling properties with JJJ and ttt we find a simple building pattern in 1D and show that every spectral feature can be uniquely assigned by a spinon and holon momentum. We find two types of low-energy excitations: A band with energy scale JJJ and high spectral weight disperses upwards in the interior part of the Brillouin zone and reaches EF{E}_{F}EF​ at kF,{k}_{F},kF​, and a band with energy scale ttt and low spectral weight disperses downwards in the outer part of the zone, touching EF{E}_{F}EF​ at 3kF.{3k}_{F}.3kF​. An analogous analysis of the 2D case at half-filling shows that the ttt band exists also in this case, but is diffuse and never reaches the Fermi energy. For the doped case in 2D the picture is more reminiscent of 1D; in particular, the main band'' with a dispersion $\ensuremath{\propto}J$ and the shadow band'' with energy scale ttt can be identified also in this case. This leads us to propose that the shadow bands discovered by Aebi et al. in Bi2212 are the 2D analog of the 3kF{3k}_{F}3kF​ singularity in 1D systems and unrelated to antiferromagnetic spin fluctuations.
Calculations of the one-electron spectral function of the $t\ensuremath{-}J$ model on a two-dimensional square lattice are described. A large-N\mathcal{N}N generalization of the $t\ensuremath{-}J$ model is used to develop 1/N1/\mathcal{N}1/N expansions, and the $t\ensuremath{-}J$ model constraint is enforced by slave bosons. The saddle point about which the 1/N1/\mathcal{N}1/N expansion is carried out is chosen to be uniform in both space and time, and self-energies are calculated to next-to-leading order in 1/N1/\mathcal{N}1/N as in the work of Z. Wang et al. [Phys. Rev. Lett. 67, 2733 (1991)]. The results of computations of the one-electron electron spectral functions for wave vectors throughout the Brillouin zone are presented for several values of the exchange coupling J/tJ/tJ/t and doping $\ensuremath{\delta}$. A sharp dispersive quasiparticle peak is found near the Fermi energy. Additional spectral weight occurs at lower frequencies, and this arises from features in the normal self-energy. These features are qualitatively similar to the self-energy obtained by Kampf and Schrieffer [Phys. Rev. B 41, 6399 (1990)] from a parametrized model of an electron coupled to antiferromagnetic spin fluctuations that leads to shadow band structure in the one-electron spectral function.
We examine spectral properties of doped holes dressed with surrounding spin cloud in the t-J model. These composite-hole excitations well characterize prominent band structures in the angle-resolved photoemission spectrum. In one-dimensional (1D) case at half-filling, we identify the composite operators that separately pick up the spinon and holon branches, respectively. After hole doping, we find that the composite hole excitations with string-like spins tend to be localized at k=π/2 in the momentum space. This means that such composite excitations should be actual electronic excitations, since the spinon and holon branches merge together at this momentum. In 2D case, we find that the composite excitations with more non-local spin fluctuation have stronger intensity near the Fermi level. The composite band structure along diagonal (0,0)-(π,π) direction in 2D has some similarity to that in 1D, and such non-local spin fluctuation plays an important role on the formation of the pseudogap in high-Tc cuprates.
The effect of a spin gap on the photoemission spectral functions is studied in the one-dimensional t - J X X Z model. We find that spinon bands show up in the spectral functions but holon bands are obscured in the spin-gap cases. The reason for this is studied using a simple interpretation of the spectral functions, which is a convolution between the spectral function of spinless fermions and a spin excitation weight Z ( Q ). The spin gap suppresses the singularity of Z ( Q ), and as a result, only the holon bands are obscured. It is also shown that the spinon peaks lie along a cosine band and extend over the region | k |> k F . Finally, the momentum-dependent critical exponents of the power-law singularity at the spinon bands are determined.
We theoretically study photoemission spectra for photodoped one-dimensional Mott insulators that can host excitons, and show that their spectral characteristics differ qualitatively from those of photodoped semiconductors. In conventional semiconductors, photoemission spectra are well understood; free charge carriers generate spectral weight near the bottom of the conduction band, while the formation of excitons leads to replica features of the valence band appearing inside the band gap. In one-dimensional Mott insulators, on the other hand, strong correlations give rise to fractionalized elementary excitations-spinons, holons, and doublons-which fundamentally modify the photoemission response. We find that when photodoped carriers, i.e., doublons and holons, remain unbound, the photoemission spectrum directly reflects the dispersion of spinons, i.e., magnetic elementary excitations. In contrast, when a doublon and a holon form an excitonic bound state, replica structures of the lower Hubbard band emerge inside the Mott gap, carrying contributions from both spinon and holon excitations. Importantly, the distribution of the in-gap signal depends sensitively on the degree of doublon-holon binding. The origin of these spectral features is clarified through a combination of exact diagonalization and the slave-particle approach. These results indicate that photoemission from photoinduced carriers and excitons in strongly correlated electron systems can provide information on magnetic properties and carrier-binding properties.
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 Ap{\mathit{A}}_{\mathbf{p}}Ap​(\ensuremath{\omega}) is momentum dependent. Using Ap{\mathit{A}}_{\mathbf{p}}Ap​(\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.
We present an exact diagonalization study of the doping dependence of the single-particle Green's function in 16-, 18-, and 20-site clusters of the t-J model. We find evidence for the validity of the rigid-band picture starting from the half-filled case: upon doping, the topmost states of the quasiparticle band observed in the photoemission spectrum at half-filling cross the chemical potential and reappear as the lowermost states of the inverse photoemission spectrum. Features in the inverse photoemission spectra, which are inconsistent with the rigid-band picture, are shown to originate from the nontrivial point-group symmetry of the ground state with two holes, which enforces different selection rules than at half-filling. Deviations from rigid-band behavior which lead to the formation of a large Fermi surface in the momentum distribution are found to occur at energies far from the chemical potential. A Luttinger Fermi surface and a nearest-neighbor hopping band do not exist.