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arXiv:cond-mat/9604093 · Physical review. B, Condensed matter

Theory for dynamical short-range order and Fermi surface volume in strongly correlated systems

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

Published Aug 1, 1996• 21 citations
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Abstract

Using the fluctuation exchange approximation of the one-band Hubbard model, we discuss the origin of the changing Fermi surface volume in underdoped cuprate systems due to the transfer of occupied states from the Fermi surface to its shadow, resulting from strong dynamical antiferromagnetic short-range correlations. The momentum and temperature dependence of the quasiparticle scattering rate shows unusual deviations from the conventional Fermi-liquid-like behavior. Their consequences for the changing Fermi surface volume are discussed. Here, we investigate in detail which scattering processes might be responsible for a violation of the Luttinger theorem. Finally, we discuss the formation of hole pockets near half filling. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.4336

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Using the fluctuation exchange approximation of the one-band Hubbard model, we discuss the origin of the changing Fermi surface volume in underdoped cuprate systems due to the transfer of occupied states from the Fermi surface to its shadow, resulting from strong dynamical antiferromagnetic short-range correlations. The momentum and temperature dependence of the quasiparticle scattering rate shows unusual deviations from the conventional Fermi-liquid-like behavior. Their consequences for the changing Fermi surface volume are discussed. Here, we investigate in detail which scattering processes might be responsible for a violation of the Luttinger theorem. Finally, we discuss the formation of hole pockets near half filling. \textcopyright{} 1996 The American Physical Society.
Though most fermionic Mott insulators order at low temperatures, ordering is ancillary to their insulating behavior. Our emphasis here is on disentangling ordering from the intrinsic strongly correlated physics of a doped half-filled band. To this end, we focus on the two-dimensional Hubbard model. Because the charge gap arises from on-site correlations, we have been refining the nonperturbative approach of Matsumoto and Mancini [Phys. Rev. B 55, 2095 (1997)] which incorporates local physics. Crucial to this method is a self-consistent two-site dynamical cluster expansion which builds in the nearest-neighbor energy scale J. At half-filling, we find that the spectral function possesses a gap of order U and is devoid of any coherent quasiparticle peaks although ordering or charge fractionalization are absent. At low temperatures, local antiferromagnetic correlations emerge. In the doped case, we find that the Fermi surface exceeds the Luttinger volume. The breakdown of Luttinger's theorem in the underdoped regime is traced both to the dynamically generated Mott gap as well to a nonvanishing of the imaginary part of the self-energy at the Fermi level. Spectral weight transfer across the Mott gap also emerges as a ubiquitous feature of a doped Mott insulator and suggests that high- and low-energy scales are inseparable. Additionally in the underdoped regime, we find that a pseudogap exists in the single-particle density of states as well as in the heat capacity. The pseudogap (which is set by the energy scale t2/U){t}^{2}/U)t2/U) is argued to be a ubiquitous feature of a lightly doped Mott state and simply represents the fact that hole transport involves double occupancy. In analogy with the Mott gap and antiferromagnetism, we propose that ordering may also accompany the formation of a pseudogap. We suggest a current pattern within a one-band model that preserves translational but breaks time-reversal symmetry along the canonical x and y axes but not along $x=\ifmmode\pm\else\textpm\fi{}y$ that is consistent with the experimental observations. Finally, we show that the Hall coefficient in a doped Mott insulator must change sign at a doping level x<1/3.x<1/3.x<1/3. The sign change is tied to a termination of strong correlation physics in the doped Mott state.
We calculate the Fermi surface of electrons in hole-doped, extended ttt-JJJ models on a square lattice in a regime where no long-range antiferromagnetic order is present, and no symmetries are broken. Using the ``spinon-dopon'' formalism of Ribeiro and Wen, we show that short-range antiferromagnetic correlations lead to a reconstruction of the Fermi surface into hole pockets which are not necessarily centered at the antiferromagnetic Brillouin zone boundary. The Brillouin zone area enclosed by the Fermi surface is proportional to the density of dopants away from half-filling, in contrast to the conventional Luttinger theorem, which counts the total electron density. This state realizes a ``fractionalized Fermi liquid'' (FL*), which has been proposed as a possible ground state of the underdoped cuprates; we note connections to recent experiments. We also discuss the quantum phase transition from the FL* state to the Fermi liquid state with long-range antiferromagnetic order.
We model the underdoped cuprates using fermions moving in a background with local antiferromagnetic order. The antiferromagnetic order fluctuates in orientation, but not in magnitude, so that there is no long-range antiferromagnetism, but a ``topological'' order survives. The normal state is described as a fractionalized Fermi liquid (FL*), with electronlike quasiparticles coupled to the fractionalized excitations of the fluctuating antiferromagnet. The electronic quasiparticles reside near pocket Fermi surfaces enclosing total area xxx (the dopant density), centered away from the magnetic Brillouin zone boundary. The violation of the conventional Luttinger theorem is linked to a ``species doubling'' of these quasiparticles. We describe phenomenological theories of the pairing of these quasiparticles, and show that a large class of mean-field theories generically displays a nodal-antinodal ``dichotomy'': The interplay of local antiferromagnetism and pairing leads to a small gap near the nodes of the ddd-wave pairing along the Brillouin zone diagonals, and a large gap in the antinodal region.
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-Tc{T}_{c}Tc​ 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.
We find marginal-Fermi-liquid- (MFL) like behavior in the Hubbard model on a square lattice for a range of hole doping and on-site interaction parameter U. Thereby we use a self-consistent projection operator method. It enables us to compute the momentum and frequency dependence of the single-particle excitations with high resolution. The Fermi surface is found to be holelike in the underdoped regime and electronlike in the overdoped regime. Our calculations concern normal state properties of the system. When a comparison is possible, we find consistency with finite temperature quantum Monte Carlo results. We also find a discontinuous change with doping concentration from a MFL to a Fermi-liquid behavior resulting from a collapse of the lower Hubbard band. This renders Luttinger's theorem inapplicable in the underdoped regime.
We have investigated the evolution of the electronic properties of the t-t'-U Hubbard model with hole doping and temperature. Due to the shape of the Fermi surface, scattering from short wavelength spin fluctuations leads to strongly anisotropic quasi-particle scattering rates at low temperatures near half-filling. As a consequence, significant variations with momenta near the Fermi surface emerge for the spectral functions and the corresponding ARPES signals. This behavior is quite in contrast to the intermediate doping regime and we discuss the possible relevance of our results for the interpretation of photoemission spectra in cuprate superconductors at different hole doping levels.