Optical Conductivity in the Copper Oxide Materials

The frequencyand temperature-dependent optical conductivity of the copper oxide materials in the underdoped and optimal doped regimes are studied within the t-J model. The conductivity spectrum shows the unusual behavior at low energies and anomalous midinfrared peak in the low temperatures. However, this midinfrared peak is severely depressed with increasing temperatures, and vanishes at higher temperatures. 71.27.+a, 72.10.-d, 74.72.-h Typeset using REVTEX ∗Regular Associate Member of the Abdus Salam International Centre for Theoretical Physics 1 After ten years of intense experimental study of the copper oxide superconductors, a significant body of reliable and reproducible data has been accumulated by using many probes [1,2], which shows that the most remarkable expression of the nonconventional physics of copper oxide materials is found in the normal-state [1,2]. The normal-state properties exhibit a number of anomalous properties in the sense that they do not fit in the conventional Fermi-liquid theory, and some properties mainly depend on the extent of dopings [1,2]. Among the striking features of the anomalous properties stands out the extraordinary optical conductivity [3]. The frequencyand temperature-dependent optical conductivity is a powerful probe for systems of interacting electrons, and provides very detailed information of the excitations, which interact with carriers in the normal-state and might play an important role in the superconductivity [3]. The optical conductivity of the copper oxide materials in the underdoped and optimally doped regimes has been extensively studied [3–6], and the experimental results indicate that the optical conductivity spectrum shows unusual behavior at low energies and anomalous midinfrared band in the charge-transfer gap, which is inconsistent with the conventional electron-phonon scattering mechanism. Since the undoped copper oxide materials are antiferromagnetic Mott insulators, and upon doping with holes in the copper oxide sheets, the antiferromagnetic long-range-order (AFLRO) disappears and superconductivity emerges as the ground state [2], many researchers believe that the essential physics is contained in the doped antiferromagnets [7,8], which may be effectively described by the two-dimensional (2D) t-J model acting on the space with no doubly occupied sites. In spite of its simple form the t-J model proved to be very difficult to analyze, analytically as well as numerically, because of the electron single occupancy on-site local constraint. The local nature of the constraint is of primary importance, and its violation may lead to some unphysical results [9]. Recently a fermion-spin theory based on the charge-spin separation has been proposed to incorporate this constraint [10]. The main advantage of this approach is that the electron on-site local constraints can be treated exactly in analytical calculations. Within the fermion-spin theory, we [11] have shown that AFLRO vanishes around doping δ = 5% for an reasonable value of the parameter 2 t/J = 5. The mean-field theory in the underdoped and optimally doped regimes without AFLRO has been developed [12], which has been applied to study the photoemission, electron dispersion and electron density of states in the copper oxide materials, and the results are qualitatively consistent with experiments and numerical simulations. In this paper, we consider fluctuations around this mean-field solution to study the optical conductivity, and show that the result within the fermion-spin formalism exhibits a behavior similar to that seen in the experiments and numerical simulations. We begin with the t-J model defined on a square lattice, H = −t ∑ 〈ij〉σ C iσCjσ + h.c.− μ ∑