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arXiv:cond-mat/0606633 · Physical Review B

Spectral weights, d -wave pairing amplitudes, and particle-hole tunneling asymmetry of a strongly correlated superconductor

Chung-Pin Chou, T. K. Lee, Chang-Ming Ho

Published Sep 13, 2006• 23 citations
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Abstract

The spectral weights (SW's) for adding and removing an electron of the Gutzwiller projected $d$-wave superconducting (SC) state of the $t\text{\ensuremath{-}}J$-type models are studied numerically on finite lattices. We restrict the study to the uniform system but exactly treat the strong correlation between electrons, we show that the product of weights is equal to the pairing amplitude squared, the same as in the weakly coupled case. In addition, we derive a rigorous relation of SW with doping in the electron doped system and obtain particle-hole asymmetry of the conductance-proportional quantity within the SC gap energy and, also, the anticorrelation between gap sizes and peak heights observed in tunneling spectroscopy on high ${T}_{c}$ cuprates.

DOI
10.1103/physrevb.74.092503

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The spectral weights (SW's) for adding and removing an electron of the Gutzwiller projected ddd-wave superconducting (SC) state of the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J-type models are studied numerically on finite lattices. We restrict the study to the uniform system but exactly treat the strong correlation between electrons, we show that the product of weights is equal to the pairing amplitude squared, the same as in the weakly coupled case. In addition, we derive a rigorous relation of SW with doping in the electron doped system and obtain particle-hole asymmetry of the conductance-proportional quantity within the SC gap energy and, also, the anticorrelation between gap sizes and peak heights observed in tunneling spectroscopy on high Tc{T}_{c}Tc​ cuprates.
We examine the strong correlation effects of the d-wave superconducting state by including the Gutzwiller projection for no electron double occupancy at each lattice site. The spectral weights (SW's) for adding and removing an electon on the projected superconducting state, the ground state of the 2-dimensional t-t'-t-J model with moderate doped holes describing the high Tc cuprates, are studied numerically on finite lattices and compared with the observation made by low-temperature tunneling (particle asymmetry of tunneling conductance) and angle-resolved photoemission (SW transfer from the projected Fermi liquid tate) spectoscopies. The contast with the dwave case without projection is alo presented.
We study the electronic structure of a strongly correlated d-wave superconducting state. Combining a renormalized mean field theory with direct calculation of matrix elements, we obtain explicit analytical results for the nodal Fermi velocity upsilon(F), the Fermi wave vector k(F), and the momentum distribution n(k) as a function of hole doping in a Gutzwiller projected d-wave superconductor. We calculate the energy dispersion E(k) and spectral weight of the Gutzwiller-Bogoliubov quasiparticles and find that the spectral weight associated with the quasiparticle excitation at the antinodal point shows a nonmonotonic behavior as a function of doping. Results are compared to angle resolved photoemission spectroscopy of the high-temperature superconductors.
We systematically examine the asymmetry of the electronic states in the hole- and electron-doped cuprates by using a $t\text{\ensuremath{-}}J$ model with the second-neighbor hopping ${t}^{\ensuremath{'}}$ and third one ${t}^{\ensuremath{''}}$ (the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}J$ model). Numerically exact diagonalization method is employed for a 20-site square lattice. We impose twisted boundary conditions (BC) instead of standard periodic BC. For static and dynamical correlation functions, averaging procedure over the twisted BC is used to reduce the finite-size effect. We find that antiferromagnetic spin correlation remains strong in electron doping in contrast to the case of hole doping, being similar to the case of the periodic BC. This leads to a remarkable electron-hole asymmetry in the dynamical spin structure factor and two-magnon Raman scattering. By changing the twist, the single-particle spectral function is obtained for all momenta in the Brillouin zone. Examining the spectral function in detail, we find a gap opening at around the $\mathbf{k}=(\ensuremath{\pi},0)$ region for 10% doping of holes (the carrier concentration x=0.1x=0.1x=0.1), leading to a Fermi arc that is consistent with experiments. In electron doping, however, a gap opens at around $\mathbf{k}=(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ and persists up to x=0.2x=0.2x=0.2, being correlated with the strength of the antiferromagnetic correlation. We find that the magnitude of the gaps is sensitive to ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$. A pseudogap is also seen in the optical conductivity for electron doping, and its magnitude is found to be the same as that in the spectral function. We compare calculated quantities with corresponding experimental data, and discuss similarities and differences between them as well as their implications.
This thesis is devoted to a theoretical study of high-temperature superconductivity from the viewpoint of a doped Mott insulator. To this end, the square-lattice t-J model is analyzed by variational and mean-field approaches. The thesis focuses on the construction of excitations and on spectral properties in the framework of Anderson's concept of resonating-valence-bond wavefunctions. The quantum dimer model as a toy model for the resonating-valence-bond phase of Mott insulators is also explored. In the first part of the thesis, the single-particle Green's functions in the superconducting phase are analyzed using Gutzwiller-projected variational wavefunctions for the t-J model. It is found that the overall spectral weight is reduced by a momentum-dependent renormalization, and that the projection produces a particle-hole asymmetry in the renormalization of the spectral weights. The second part analyzes the Green's functions in the pseudogap phase of the cuprates within an SU(2) mean-field approach where the order parameter fluctuates between the d-wave superconductor and the non-superconducting staggered-flux state. The model predicts a photoemission spectrum with an asymmetric gap structure interpolating between the superconducting gap centered at the Fermi energy and the asymmetric staggered-flux gap. This gap asymmetry changes sign at the "hot-spots" where the Fermi surface crosses the diagonal (0,π)-(π,0). In the last part of the thesis, single hole and vortex excitations in the liquid phase of the triangular-lattice Rokhsar-Kivelson quantum dimer model are considered. It is found that the motion of a hole bound to a topological excitation is strongly constrained due to interference effects.
We analyze the electronic Green's functions in the superconducting ground state of the $t\text{\ensuremath{-}}J$ model using Gutzwiller-projected wave functions, and compare them to the conventional BCS form. Some of the properties of the BCS state are preserved by the projection: the total spectral weight is continuous around the quasiparticle node and approximately constant along the Fermi surface. On the other hand, the overall spectral weight is reduced by the projection with a momentum-dependent renormalization, and the projection produces electron-hole asymmetry in renormalization of the electron and hole spectral weights. The latter asymmetry leads to the bending of the effective Fermi surface, which we define as the locus of equal electron and hole spectral weight.