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Physical review. B, Condensed matter

Optical absorption in the canted antiferromagnetic phase of a t - J model

G. C. Psaltakis

Published Jan 1, 1992• 9 citations
Publisher

Abstract

We calculate the real part of the finite-frequency conductivity, i.e., the optical absorption, in the canted antiferromagnetic phase of a t-J model using a suitable 1/N expansion. We find that below a characteristic crossover frequency \ensuremath{\Delta} the absorption is very small, while above \ensuremath{\Delta} it rises sharply to a broad maximum, in qualitative agreement with recent infrared absorption experiments in doped antiferromagnets. This crossover frequency is identified with an energy gap developing upon hole doping in one of the two branches of elementary excitations, at the corner of the square Brillouin zone.

DOI
10.1103/physrevb.45.539

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A finite-size scaling analysis of the spectral function and of the optical conductivity of a single hole moving in an antiferromagnetic background is performed. It is shown that both the low-energy quasiparticle peak and the broad higher-energy structure are robust with increasing cluster size from 4\ifmmode\times\else\texttimes\fi{}4 to \ensuremath{\surd}26 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}26 sites. In the absence of spin fluctuations, for most static or dynamical quantities saturation occurs when the size exceeds a characteristic size ${\mathit{N}}_{\mathit{c}}$(${\mathit{J}}_{\mathit{z}}$). Typically, 16- and 26-site clusters give reliable results for ${\mathit{J}}_{\mathit{z}}$>0.75 and ${\mathit{J}}_{\mathit{z}}$>0.3, respectively. The hole optical mass is shown to be very large (>20) in agreement with the small bandwidth. Due to the energy gap to flip a spin in the vicinity of a hole, a small gap \ensuremath{\propto}${\mathit{J}}_{\mathit{z}}$ separates the low-energy \ensuremath{\delta} function from the rest of the spectrum in the dynamical correlation functions. On the other hand, with ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ this gap seems to disappear with increasing system size as one would expect since the spin waves are gapless in the thermodynamic limit. The large momentum dependence of the quasiparticle weight in the isotropic case is inconsistent with a string picture but agrees well with the self-consistent Born approximation.An accurate estimation of the higher-energy part of the spectral functions of the t-J model can be made for momenta close to (0,0) or (\ensuremath{\pi},\ensuremath{\pi}); it consists of a broad featureless band. For momenta close to the Fermi surface, no evidence for excited string states is found. This may be either because the string scenario breaks down or because exact calculations at momenta near (\ensuremath{\pi}/2,\ensuremath{\pi}/2) are limited by the differing geometries of the finite clusters. In the Ising limit, the spectral function also depends crucially on the momentum, but a feature resembling a string excitation is seen for momenta close to (0,0). Our data on the finite-frequency optical conductivity of a single hole in the t-J model reveal that the total spectral weight at finite frequency has a strong size dependence and decreases with increasing size (for J not too small). This suggests that the optical mass and the optical absorption of the t-J model may have been overestimated in the past.

arXiv:cond-mat/9212010•Physical review. B, Condensed matter•Jun 1, 1993•54 citations
We calculate the real part of the finite-frequency conductivity, i.e., the optical absorption, in the canted antiferromagnetic phase of a t-J model using a suitable 1/N expansion. We find that below a characteristic crossover frequency \ensuremath{\Delta} the absorption is very small, while above \ensuremath{\Delta} it rises sharply to a broad maximum, in qualitative agreement with recent infrared absorption experiments in doped antiferromagnets. This crossover frequency is identified with an energy gap developing upon hole doping in one of the two branches of elementary excitations, at the corner of the square Brillouin zone.
The phase diagram of a t-t'-J model on a square lattice has been determined within a suitable 1/N expansion and shown to exhibit a phase-modulated antiferromagnetic (AF) ground state close to half-filling. Here we calculate the real part of the finite-frequency conductivity \ensuremath{\sigma}(\ensuremath{\omega}), i.e., the optical absorption, in the AF state and find a structureless broadband regime at low frequencies, in qualitative agreement with infrared absorption experiments in doped antiferromagnets. In particular, the limiting value \ensuremath{\sigma}(\ensuremath{\omega}\ensuremath{\rightarrow}0) is finite, at finite hole doping, due to the diffusion character of the relevant low-energy quasiparticle states at the corner of the square Brillouin zone.
The dynamics of magnetic fluctuations in the canted antiferromagnetic phase of a t-J model is studied within a suitable 1/N expansion. We calculate the dynamical structure factor and assess the effect of hole doping on the excitation spectrum, the staggered antiferromagnetic moment, and the perpendicular uniform ferromagnetic moment. The average long-wavelength excitation energies in the transverse direction are shown to soften with increasing hole concentration, in qualitative agreement with recent neutron-scattering experiments in doped antiferromagnets.
We investigate the extended t-J model (which may include a small next-nearest-neighbor antiferromagnetic coupling or a small hole-hole nearest-neighbor repulsion) by exact-diagonalization techniques. The calculation is done for one and two holes on a 4\ifmmode\times\else\texttimes\fi{}4 torus with arbitrary twisted boundary conditions. The role of the boundary conditions on the ground-state energy, the band width, the charge stiffness, and the optical conductivity is extensively studied. In the two-dimensional space of the twist angles (to be viewed as fluxes through the holes of the torus) the ground-state energy surface exhibits multiple level crossings and may present, locally, a negative curvature (or stiffness) characteristic of a paramagnetic behavior. For two holes and sufficiently large J/t (J/t>0.7) the minima of the energy surface in the parameter space of the fluxes are separated by half a flux quantum. The optical conductivity is calculated by averaging over the boundary conditions in order to minimize finite-size effects and to converge more rapidly toward the thermodynamic limit. We find three different contributions to the optical conductivity; (i) a Drude peak at \ensuremath{\omega}=0, (ii) a broad absorption band in the range J2t, and (iii) a tail extending to larger frequencies (2t7t) associated to the diffusive character of the hole states at these energies.Typically, at low doping density (6%) for a wide range of J/t, and at intermediate doping (12%) for small J/t, these three components account for roughly 30%, 50%, and 20% of the total spectral weight, respectively. At small ratio J/t, both Drude weight and finite-frequency absorption scale almost proportionally with the doping density. However, with increasing J/t, the effective hole-hole attraction (for 12% doping) leads to a transfer of weight from finite frequency to zero frequency. In contrast to the quasiparticle mass, in the J/t\ensuremath{\rightarrow}0 limit, the optical mass defined through the weight of the Drude \ensuremath{\delta}-function peak does not increase like \ensuremath{\sim}t/J but, rather, approaches a limit around \ensuremath{\sim}5. We discuss our results in connection with the optical experiments in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates and suggest that the observed mid-infrared band is due to the strong coupling between the mobile holes and the spin excitations of the Mott insulator, as expected from a description in terms of the t-J Hamiltonian.
To discuss the interplay of electronic and lattice degrees of freedom in systems with strong Coulomb correlations we have performed an extensive numerical study of the two-dimensional Holstein $t\ensuremath{-}J$ model. The model describes the interaction of holes, doped in a quantum antiferromagnet, with a dispersionsless optical phonon mode. We apply finite-lattice Lanczos diagonalization, combined with a well-controlled phonon Hilbert space truncation, to the Hamiltonian. The focus is on the dynamical properties. In particular we have evaluated the single-particle spectral function and the optical conductivity for characteristic hole-phonon couplings, spin exchange interactions, and phonon frequencies. The results are used to analyze the formation of lattice hole polarons in great detail. Links with experiments on layered perovskites are made. In addition, we compare the Chebyshev recursion and maximum entropy algorithms, used for calculating spectral functions, with standard Lanczos methods.
We study the real part of the optical conductivity in the t-J model using the slave-boson technique and the large-N expansion to the next-to-leading order in 1/N. The conductivity falls off at a slower rate than predicted by the Drude theory due to the coupling to the low-energy spin excitation. The absorptions from the mid-infrared (MIR) range to higher frequency (\ensuremath{\sim}1 eV) arise from the incoherent motion of the charge carrier. We compare our results to finite-cluster exact-diagonalization studies and to experimental studies in the copper oxide system.
A finite-size scaling analysis of the spectral function and of the optical conductivity of a single hole moving in an antiferromagnetic background is performed. It is shown that both the low-energy quasiparticle peak and the broad higher-energy structure are robust with increasing cluster size from 4\ifmmode\times\else\texttimes\fi{}4 to \ensuremath{\surd}26 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}26 sites. In the absence of spin fluctuations, for most static or dynamical quantities saturation occurs when the size exceeds a characteristic size Nc{\mathit{N}}_{\mathit{c}}Nc​(Jz{\mathit{J}}_{\mathit{z}}Jz​). Typically, 16- and 26-site clusters give reliable results for Jz{\mathit{J}}_{\mathit{z}}Jz​>0.75 and Jz{\mathit{J}}_{\mathit{z}}Jz​>0.3, respectively. The hole optical mass is shown to be very large (>20) in agreement with the small bandwidth. Due to the energy gap to flip a spin in the vicinity of a hole, a small gap \ensuremath{\propto}Jz{\mathit{J}}_{\mathit{z}}Jz​ separates the low-energy \ensuremath{\delta} function from the rest of the spectrum in the dynamical correlation functions. On the other hand, with ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ this gap seems to disappear with increasing system size as one would expect since the spin waves are gapless in the thermodynamic limit. The large momentum dependence of the quasiparticle weight in the isotropic case is inconsistent with a string picture but agrees well with the self-consistent Born approximation.An accurate estimation of the higher-energy part of the spectral functions of the t-J model can be made for momenta close to (0,0) or (\ensuremath{\pi},\ensuremath{\pi}); it consists of a broad featureless band. For momenta close to the Fermi surface, no evidence for excited string states is found. This may be either because the string scenario breaks down or because exact calculations at momenta near (\ensuremath{\pi}/2,\ensuremath{\pi}/2) are limited by the differing geometries of the finite clusters. In the Ising limit, the spectral function also depends crucially on the momentum, but a feature resembling a string excitation is seen for momenta close to (0,0). Our data on the finite-frequency optical conductivity of a single hole in the t-J model reveal that the total spectral weight at finite frequency has a strong size dependence and decreases with increasing size (for J not too small). This suggests that the optical mass and the optical absorption of the t-J model may have been overestimated in the past.