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Physical review. B, Condensed matter

Non-Fermi-liquid behavior for holes in doped two-dimensional antiferromagnets

Jian‐Xin Li, Chang-De Gong

Published Mar 1, 1995• 7 citations
Publisher

Abstract

Spin and hole excitations are investigated in the doped two-dimensional (2D) antiferromagnets described by the t-J model based on the spin-wave approximation. The polarizability of spin excitations is found to be consistent with the marginal-Fermi-liquid hypothesis. As a consequence, the imaginary part of the self-energy for holes scattered by the spin excitations is demonstrated to give a linear dependence in temperature T (for \ensuremath{\omega}T) and in frequency \ensuremath{\omega} (for \ensuremath{\omega}>T).

DOI
10.1103/physrevb.51.6343

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arXiv:0907.3058•Jul 17, 2009•0 citations
Spin and hole excitations are investigated in the doped two-dimensional (2D) antiferromagnets described by the t-J model based on the spin-wave approximation. The polarizability of spin excitations is found to be consistent with the marginal-Fermi-liquid hypothesis. As a consequence, the imaginary part of the self-energy for holes scattered by the spin excitations is demonstrated to give a linear dependence in temperature T (for \ensuremath{\omega}T) and in frequency \ensuremath{\omega} (for \ensuremath{\omega}>T).
Kinetic properties of a two-dimensional model of fermions interacting with antiferromagnetic spin excitations near the quantum critical point are considered. The temperature or doping are assumed to be sufficiently high, such that the pseudogap does not appear. In contrast to standard spin-fermion models, it is assumed that there are intrinsic inhomogeneities in the system suppressing space correlations of the antiferromagnetic excitations. It is argued that the inhomogeneities in the spin excitations in the ``strange metal'' phase can be a consequence of the existence of ``$\ensuremath{\pi}$-shifted'' domain walls in the doped antiferromagnetic phase. Averaging over the inhomogeneities and calculating physical quantities such as resistivity and some others one can explain unusual properties of cuprates unified under the name ``marginal Fermi liquid.'' The dependence of the slope of the linear temperature dependence of the resistivity on doping is compared with experimental data.
In the Wigner-Jordan (WJ) fermion representation of quantum spins with antiferromagnetic interaction, the WJ fermions always fill half of the total available states, and their energy spectrum possesses a particle-hole symmetry. These two intrinsic properties of the WJ representation, together with a finite density of states at small WJ-fermion excitation energy, give rise to the marginal-Fermi-liquid behavior of the charge carriers when they are scattered by the WJ fermions. The finite density of states of the WJ fermions at zero excitation energy is demonstrated for the defected quantum antiferromagnetic Heisenberg model in a square lattice.
We calculate the Green's function, particle-hole susceptibility and Cooper pair susceptibility of a 2D electron gas with long range current-current interactions, using Haldane bosonization scheme. We find Luttinger Liquid properties of weakly decaying power-law tails in the spectral function and a Kohn anomaly in the 2$k\sb{F}$ particle-hole susceptibility. At finite temperature, the system exhibits more radical departure from Fermi Liquid. The specific heat was determined being linearly proportional to temperature. The strong correlations of spins and holes are demonstrated in the 2D t-J model of spin-boson and hole-fermion, through the instability against charge ordering we find from our charge susceptibility calculation of bubble and ladder diagrams. We calculate the linear-T dependence of resistivity from the hole self-energy to the second order. The excitation spectra of holon and spinon found from the self-energy calculations agree with the mean-field results to that order.
The hole dynamics in a quantum antiferromagnetic background for a small doping concentration is studied within the t-J model description. The noncrossing approximation for the hole self-energy is used. The correct quasiparticle pole structure (without artificial broadening) in the spectral density function is employed. Dyson's equation for the hole Green's function is solved numerically by introducing a lattice in momentum space. The evolution of the density of states and the momentum-distribution function for holes is investigated as a function of hole-magnon coupling constant t at fixed J. The momentum distribution function shows a sharp drop at the Fermi surface for several different hole-magnon coupling constants. This indicates the validity of the Fermi liquid description for the t-J model in the low doping concentration. The volume (surface) enclosed by the Fermi surface (curve) is found to be invariant for all the coupling strengths we have studied. The incoherent spectrum below the chemical potential in the density of states becomes more significant for stronger interaction constants. These features numerically verify Luttinger's theorem for a small density of doped holes in the t-J model. The optical conductivity is computed using the lowest-order diagrams. As the hole-magnon coupling constant t increases, absorption becomes stronger at \ensuremath{\omega}\ensuremath{\simeq}2J, the characteristic frequency for spin waves. This feature may be associated with the experimentally observed midinfrared absorption band in underdoped cuprates.
We study the finite-temperature Fermi-liquid to non-Fermi-liquid crossover in the two-dimensional Hubbard model for a range of dopings using the self-consistent ladder dual fermion method. We consider relatively high temperatures where by comparing the single-particle self-energy and the two-particle spin susceptibility we identify a suppression of the density of states near the Fermi level caused by a quasi-antiferromagnetic behavior that is itself characterized by a long, but finite, correlation length scale which we extract. We compute the single-particle self-energy, and the charge/spin susceptibilities for the entire doping range at relatively high temperature, and also for the half-filled weak-coupling case at relatively low temperatures. We perform fluctuation diagnostics to decompose the single-particle self-energy into scattering qqq-vector and bosonic frequency contributions in the spin channel. Within this framework we find that the key contributions to the single-particle self-energy that give non-Fermi-liquid character show complicated dependence on zero, positive, and negative frequency bosonic modes. We find that for a nominal choice of ${t}^{\ensuremath{'}}$ that electron- and hole-doped systems with similar Fermi-liquid character have distinct spin and charge susceptibility and distinct spin-fluctuation diagnostics spectra.
The effect of doping in the two-dimensional Hubbard model is studied within finite temperature exact diagonalization combined with cluster dynamical mean field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green's function onto 2x2 clusters, a considerably more accurate description of the low frequency properties of the self-energy is achieved than in a pure site picture. The transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest neighbor hopping, and temperature. In particular, the self-energy component Sigma_X associated with X=(pi,0) is shown to exhibit an onset of non-Fermi-liquid behavior as the hole doping decreases below a critical value delta_c. The imaginary part of Sigma_X(omega) then develops a collective mode above E_F, which exhibits a distinct dispersion with doping. Accordingly, the real part of Sigma_X(omega) has a positive slope above E_F, giving rise to an increasing particle-hole asymmetry as the system approaches the Mott transition. This behavior is consistent with the removal of spectral weight from electron states close to E_F and the opening of a pseudogap which increases with decreasing doping. The phase diagram reveals that delta_c = 0.15 ... 0.20 for various system parameters. For electron doping, the collective mode of Sigma_X(omega) and the concomitant pseudogap are located below the Fermi energy which is consistent the removal of spectral weight from hole states just below E_F. The critical doping which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping.