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arXiv:cond-mat/9605151 · Physical review. B, Condensed matter

Optical conductivity of strongly correlated electron systems

R. Eder, P. Wróbel, Y. Ohta

Published Oct 15, 1996• 10 citations
arXivHTMLPDF

Abstract

We present an exact-diagonalization study of the frequency- and wave-vector-dependent conductivity $\ensuremath{\sigma}(\mathrm{q}, \ensuremath{\omega})$ in small clusters in the two-dimensional $t\ensuremath{-}J$ model. Unlike the related dynamical density correlation function, $\ensuremath{\sigma}(\mathrm{q}=0, \ensuremath{\omega})$ in the underdoped regime has the exchange constant $J$ as its characteristic energy scale and is dominated by a resonancelike excitation with frequency $\ensuremath{\sim}1.7J$. We interpret this as transition to a $p$-like excited state of a spin-bag-type quasiparticle (or, alternatively, a tightly bound spinon-holon pair) and show that a simple calculation based on the string picture explains the numerical results semiquantitatively. For doping levels $>~25%t$ remains the only energy scale of $\ensuremath{\sigma}(\mathrm{q}=0, \ensuremath{\omega})$.

DOI
10.1103/physrevb.54.r11034

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We present an exact-diagonalization study of the frequency- and wave-vector-dependent conductivity \ensuremathσ(q,\ensuremathω)\ensuremath{\sigma}(\mathrm{q}, \ensuremath{\omega})\ensuremathσ(q,\ensuremathω) in small clusters in the two-dimensional t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model. Unlike the related dynamical density correlation function, \ensuremathσ(q=0,\ensuremathω)\ensuremath{\sigma}(\mathrm{q}=0, \ensuremath{\omega})\ensuremathσ(q=0,\ensuremathω) in the underdoped regime has the exchange constant JJJ as its characteristic energy scale and is dominated by a resonancelike excitation with frequency \ensuremath∼1.7J\ensuremath{\sim}1.7J\ensuremath∼1.7J. We interpret this as transition to a ppp-like excited state of a spin-bag-type quasiparticle (or, alternatively, a tightly bound spinon-holon pair) and show that a simple calculation based on the string picture explains the numerical results semiquantitatively. For doping levels > 25>~25%t> 25 remains the only energy scale of \ensuremathσ(q=0,\ensuremathω)\ensuremath{\sigma}(\mathrm{q}=0, \ensuremath{\omega})\ensuremathσ(q=0,\ensuremathω).
We investigate the dynamical charge-charge correlation function and the optical conductivity in weakly doped antiferromagnets using Mori-Zwanzig projection technique. The system is described by the two-dimensional t - J model. The arising matrix elements are evaluated within a cumulant formalism which was recently applied to investigate magnetic properties of weakly doped antiferromagnets. Within the present approach the ground state consists of non-interacting hole quasiparticles. Our spectra agree well with numerical results calculated via exact diagonalization techniques. The method we employ enables us to explain the features present in the correlation functions. We conclude that the charge dynamics at weak doping is governed by transitions between excited states of spin-bag quasiparticles.
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.
The U(1) holon-pair boson theory of Lee and Salk [Phys. Rev. B 64, 052501 (2001)] is applied to investigate the quantum scaling behavior of optical conductivity in the two-dimensional systems of strongly correlated electrons. We examine the role of both the gauge field fluctuations and spin pair excitations on the $\ensuremath{\omega}∕T$ scaling behavior of the optical conductivity. It is shown that the gauge field fluctuations but not the spin pair excitations are responsible for the scaling behavior in the low-frequency region $\ensuremath{\omega}∕T⪡1$. The importance for the contribution of the nodal spinons to the Drude peak is discussed. It is shown that the $\ensuremath{\omega}∕T$ scaling behavior is manifest in the low-frequency region at low hole concentrations close to a critical concentration at which superconductivity arises at T=0KT=0\phantom{\rule{0.3em}{0ex}}\mathrm{K}T=0K.
The U(1) holon-pair boson theory of Lee and Salk(Phys. Rev. B 64, 052501 (2001)) is applied to investigate the quantum scaling behavior of optical conductivity in the two dimensional systems of strongly correlated electrons. We examine the role of both the gauge field fluctuations and spin pair excitations on the w/T scaling behavior of the optical conductivity. It is shown that the gauge field fluctuations but not the spin pair excitations are responsible for the scaling behavior in the low frequency region w/T <<1. Importance for the contribution of the nodal spinons to the Drude peak is discussed. It is shown that the w/T scaling behavior is manifest in the low frequency region at low hole concentrations close to a critical concentration at which superconductivity arises at T=0K.
We present a nonperturbative method for deriving a quasiparticle description of the low-energy excitations in the t-J model for strongly correlated electrons. Using the exact diagonalization technique we evaluated exactly the spectral functions of composite operators, which describe an electron or hole dressed by antiferromagnetic spin fluctuations as expected in the string or spin bag picture. For hole doping up to 1/8, use of the composite operators leads to a drastic simplification of the single-particle spectral function: at half-filling it takes free-particle form, for the doped case it resembles a system of weakly interacting fermions corresponding to the doped holes. We conclude that for all doping levels studied, the elementary electronic excitations next to the Fermi level are adequately described by the antiferromagnetic spin-fluctuation picture.
We present an exact diagonalization study of the dynamical spin and density correlation functions in small clusters of 2D $t\ensuremath{-}J$ model for hole dopings $\ensuremath{\le}25$%. Both correlation functions show a remarkably regular, but very different, scaling with both hole density ${\ensuremath{\rho}}_{h}$ and parameters ttt and JJJ. The density correlation function is most consistent with that of condensed bosons in a band of width $\ensuremath{\sim}t$, the spin correlation function with that of fermions in a band of width $\ensuremath{\sim}J$. We show that the familiar spin bag scenario explains these results in a natural way.