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arXiv:cond-mat/0612696 · Physical Review B

Charge dynamics in the phase string model for high- Tc superconductors

Zheng‐Cheng Gu, Zheng-Yu Weng

Published Jul 2, 2007• 5 citations
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Abstract

An understanding of the anomalous charge dynamics in the high-${T}_{c}$ cuprates is obtained based on a model study of doped Mott insulators. The high-temperature optical conductivity is found to generally have a two-component structure: a Drude-like part followed by a mid-infrared band. The scattering rate associated with the Drude part exhibits a linear-temperature dependence over a wide range of high temperature, while the Drude term gets progressively suppressed below a characteristic energy of magnetic origin as the system enters the pseudogap phase. The high-energy optical conductivity shows a resonancelike feature in an underdoped case and continuously evolves into a $1∕\ensuremath{\omega}$ tail at higher doping, indicating that they share the same physical origin. In particular, such a high-energy component is closely correlated with the $\ensuremath{\omega}$-peak structure of the density-density correlation function at different momenta, in systematic consistency with exact diagonalization results based on the $t\text{\ensuremath{-}}J$ model. The underlying physics is attributed to the high-energy spin-charge separation in the model, in which the ``mode coupling'' responsible for the anomalous charge properties is not between the electrons and some collective mode but rather between charge carriers, holons, and a topological gauge field controlled by spin dynamics, as the consequence of the strong short-range electron-electron Coulomb repulsion in the doped Mott insulator.

DOI
10.1103/physrevb.76.024501

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An understanding of the anomalous charge dynamics in the high-Tc{T}_{c}Tc​ cuprates is obtained based on a model study of doped Mott insulators. The high-temperature optical conductivity is found to generally have a two-component structure: a Drude-like part followed by a mid-infrared band. The scattering rate associated with the Drude part exhibits a linear-temperature dependence over a wide range of high temperature, while the Drude term gets progressively suppressed below a characteristic energy of magnetic origin as the system enters the pseudogap phase. The high-energy optical conductivity shows a resonancelike feature in an underdoped case and continuously evolves into a 1∕\ensuremathω1∕\ensuremath{\omega}1∕\ensuremathω tail at higher doping, indicating that they share the same physical origin. In particular, such a high-energy component is closely correlated with the \ensuremathω\ensuremath{\omega}\ensuremathω-peak structure of the density-density correlation function at different momenta, in systematic consistency with exact diagonalization results based on the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model. The underlying physics is attributed to the high-energy spin-charge separation in the model, in which the ``mode coupling'' responsible for the anomalous charge properties is not between the electrons and some collective mode but rather between charge carriers, holons, and a topological gauge field controlled by spin dynamics, as the consequence of the strong short-range electron-electron Coulomb repulsion in the doped Mott insulator.
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The optical conductivity (OC) of cuprates is studied theoretically in the low-density limit of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model taking into account the hole-lattice coupling. By developing a limited phonon basis exact diagonalization method capable of treating the lattice of largest size ever considered $(4\ifmmode\times\else\texttimes\fi{}4)$, we are able to discern the fine features of the mid-infrared (MIR) part of the OC revealing a three-peak structure. The two lowest peaks are observed in experiments and the highest one is tacitly resolved in moderately doped cuprates. Comparison of OC with the results of semianalytic approaches and detailed analysis of the calculated isotope effect indicate that the middle-energy MIR peak is of mostly magnetic origin while the lowest MIR band originates from the scattering of holes by phonons.
The optical conductivity of the 2D t−Jt-Jt−J model and the origin of electron incoherence in the high-Tc_{c}c​ cuprate superconductors: a variational study
Understanding the origin of electron incoherence is the first step toward a theoretical description of the non-Fermi liquid behavior of the high-Tc_{c}c​ cuprate superconductors. Such electron incoherence manifests itself most evidently in the non-Drude behavior of the optical response of the system and the anomalous density fluctuation behavior in the long wave length limit. The spectral weight transfer related to such dissipative response, which is absent in conventional Fermi liquid metal, has direct consequence on the dc transport property of the system in the normal state and the superfluid stiffness in the superconducting state. It is found that such electron incoherence remains significant even in the clean limit and at low temperature and thus must be attributed to the strong electron correlation effect in the cuprate superconductors. Here we study such an intrinsic effect in the 2D t−Jt-Jt−J model through the variational calculation of its optical conductivity σ(ω)σ(ω)σ(ω). We assume a resonating valence bond ground state as our starting point and find that a significant portion of the total optical spectral weight remains incoherent throughout the phase diagram. The optical absorption is found to extend all the way to an energy of the order of the bare band width. We find that both the total optical weight Kˉ\bar{K}Kˉ and the integrated incoherent optical weight III increase monotonically with doping, with their ratio Rincoh=I/KˉR_{incoh}=I/\bar{K}Rincoh​=I/Kˉ decreasing monotonically with doping. Our results indicate that the majority part of electron incoherence in the 2D t−Jt-Jt−J model can be attributed to the electron fractionalization mechanism assumed in such a treatment. We also find that the Drude weight deduced from D=Kˉ−ID=\bar{K}-ID=Kˉ−I scales linearly with hole doping, without any sign of a non-monotonic behavior in the overdoped regime.
Within the framework of the fermion-spin theory, the charge transport in the doped Mott insulators on a honeycomb lattice is studied by taking into account the pseudogap effect. It is shown that the conductivity spectrum in the low-doped regime is separated by the pseudogap into a low-energy non-Drude peak followed by a broad mid-infrared band. However, the decrease of the pseudogap with the increase of doping leads to a shift of the position of the mid-infrared band towards the low-energy non-Drude peak, and then the low-energy Drude behavior recovers in the high-doped regime. The combined results of both the doped honeycomb-lattice and square-lattice Mott insulators indicate that the two-component conductivity induced by the pseudogap is a universal feature in the doped Mott insulators.
We study electronic structure of hole- and electron-doped Mott insulators in the two-dimensional Hubbard model to reach a unified picture for the normal state of cuprate high-Tc{T}_{c}Tc​ superconductors. By using a cluster extension of the dynamical mean-field theory, we demonstrate that structure of coexisting zeros and poles of the single-particle Green's function holds the key to understand Mott physics in the underdoped region. We show evidence for the emergence of non-Fermi-liquid phase caused by the topological quantum phase transition of Fermi surface by analyzing low-energy charge dynamics. The spectra calculated in a wide range of energy and momentum reproduce various anomalous properties observed in experiments for the high-Tc{T}_{c}Tc​ cuprates. Our results reveal that the pseudogap in hole-doped cuprates has a ddd-wavelike structure only below the Fermi level while it retains non-ddd-wave structure with a fully opened gap above the Fermi energy even in the nodal direction due to a zero surface extending over the entire Brillouin zone. In addition to the non-ddd-wave pseudogap, the present comprehensive identifications of the spectral asymmetry as to the Fermi energy, the Fermi arc, and the back-bending behavior of the dispersion, waterfall, and low-energy kink, in agreement with the experimental anomalies of the cuprates, do not support that these originate from (the precursors of) symmetry breakings such as the preformed pairing and the ddd-density-wave fluctuations, but support that they are direct consequences of the proximity to the Mott insulator. Several possible experiments are further proposed to prove or disprove our zero mechanism.
The electronic $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U\text{\ensuremath{-}}J$ model for the CuO2\mathrm{Cu}{\mathrm{O}}_{2}CuO2​ plane in high-Tc{T}_{c}Tc​ superconducting cuprates is elaborated. It incorporates both charge transfer UUU and exchange correlation JJJ with direct ttt and diagonal ${t}^{\ensuremath{'}}$ hopping. Making use of the Yang concept of the off diagonal long range order (ODLRO) in the reduced density matrix of the electronic system we study the loss of quantum wave coherence (and thereby superconductivity) due to the Coulomb interaction. To this aim the second-quantized Hamiltonian of the model is translated to the phase representation with the help of the topologically constrained path integral formalism. As a result the electrons emerge as composite particles consisting of of spin-carrying neutral fermions and charged topological bosons in a form of ``flux tubes'' with the quantum phase variable dual to the local electron density. The charge carrying bose field forms a collective variable representing the correlated ``sliding'' motion of the entire electronic system. We found that the spin gap $\ensuremath{\Delta}$ which appears in one-particle spectrum is the result of valence bond pairing of neutral fermions without ODLRO and deduce the solution for $\ensuremath{\Delta}$ with ``ddd-wave'' symmetry. In the bosonic sector we derive the effective quantum rotor model along with microscopic phase stiffnesses setting the energy scale for superconductivity and point out the special role played by the diagonal hopping ${t}^{\ensuremath{'}}$. We explore the relationship of the quantum rotor phase model and the Bose-Hubbard system emphasizing the ring topology of quantum phase variable. Furthermore, we obtain the ground state phase diagrams which facilitate the Mott insulator-superconductor transition scenario. We elucidate the role of the chemical potential (doping) and the huge degeneracy of the effective bosonic system in achieving ODLRO with long-range phase coherence in the presence of large Coulomb repulsion. Finally, we discuss a number of relevant issues pertaining to the the present work which include: theoretical aspects of the hierarchy of the energy scales in cuprates, ``spin-charge separation'' concepts, ``local-pair'' and ``phase-fluctuation'' scenarios as well as experimental findings related to the role of the ``ddd-wave'' symmetry of the spin gap and diagonal hopping ${t}^{\ensuremath{'}}$ in cuprates.