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Physical review. B, Condensed matter

Optical absorption in the phase-modulated antiferromagnetic state of at-t’-Jmodel

G. C. Psaltakis

Published Feb 1, 1995• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.51.2979

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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.
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.
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.
We present a study of a t-t'-J model on a square lattice, where t' denotes hopping along the diagonal, within a suitable 1/N expansion. The T=0 phase diagram consists of conventional ferromagnetic and incommensurate (Q,Q) and (Q,0) spiral phases, in addition to an unconventional antiferromagnetic (AF) phase characterized by the usual (\ensuremath{\pi},\ensuremath{\pi}), i.e., N\'eel modulation of the spin configuration and an unusual (\ensuremath{\pi},-\ensuremath{\pi}) phase modulation. We obtain the spectrum of elementary excitations for all these phases and explicitly display the associated Goldstone-mode structure. A detailed analysis of the AF phase including leading quantum-fluctuation effects shows that it remains locally stable at small finite doping, in agreement with the observed behavior in doped antiferromagnets, as well as globally stable against phase separation for sufficiently large t'. A characteristic feature of this AF phase is an anisotropy in the velocities of its elementary excitations which is suppressed, however, at half-filling. Finally, the spin-spin dynamical structure factor in the AF phase is found to exhibit a double peak at finite doping, which reflects hybridization between the relevant transverse (magnonlike) and longitudinal (holonlike) modes, one of the peaks also being suppressed at half-filling.
Results are for finite-temperature optical conductivity \ensuremath{\sigma}(\ensuremath{\omega}) and dc resistivity \ensuremath{\rho}(T), obtained within the t-J model on a square lattice by a method based on the Lanczos diagonalization. Studying systems with N=16 or 18 sites and hole concentrations ch{\mathit{c}}_{\mathit{h}}ch​\ensuremath{\le}0.25, a thermodynamic behavior is reached for quite low temperatures. \ensuremath{\sigma}(\ensuremath{\omega}) spectra reveal a slow non-Drude falloff at large frequencies and the emergence of a broad midinfrared peak at low doping. At optimum doping \ensuremath{\rho}(T) shows nearly linear variation with T. Both quantities agree well with experimental results in cuprates.
We calculate the optical conductivity \ensuremath{\sigma}(\ensuremath{\omega}) of the Hubbard and t-J models on 10- and 16-site lattices, respectively, using a Lanczos method. Results are presented for various values of the couplings U/t, J/t, and band fillings, using free- and periodic-boundary conditions. We discuss the behavior of the kinetic energy in the ground state, the distribution of spectral weight of \ensuremath{\sigma}(\ensuremath{\omega}) between low and high energies and the sum rule. Indications of a Drude-like peak at low energy in the one-hole subspace are observed in both models. Assuming that holes behave like independent (mass-renormalized) particles in the normal state of the superconductors, our results also suggest that the optical midinfrared broadband observed experimentally can be explained by hole excitations of strongly correlated systems.
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.