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Bulletin of Materials Science

Calculations of the effects of point defects on hubbard models of high temperature superconductivity

J. W. Halleý, S Davis, Peter John Samsel, Robert Joynt

Published Aug 1, 1991• 3 citations
Publisher
DOI
10.1007/bf02747481

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The specific heat and the condensation energy of a two-dimensional Hubbard model, suitable to discuss high Tc superconductors (HTSTC), is studied taking into account hopping to first (t) and second (t2) nearest neighbors. Results for the Hubbard model show that the specific heat as a function of the temperature C(T) presents a two peaks structure (DUFFY; MOREO, 1997). The low temperature peak has been associated with spin fluctuation while the high temperature peak is related to charge fluctuation. Experimental results for the specific heat of HTSC s (LORAM et al., 2001), for instance, the YBCO and LSCO, indicate a close relation between the pseudogap and the specific heat. In the present work, we investigate the specific heat by the Green s function method within the n-pole approximation proposed by L. Roth (ROTH, 1969). The specific heat is calculated on the pseudogap and on the superconducting regions. Superconductivity with dx2−y2- wave pairing is considered following the procedure proposed by Beenen and Edwards (BEENEN; EDWARDS, 1995). The analytical expressions for the specific heat and for the condensation energy have been obtained following the formalism presented in reference (KISHORE; JOSHI, 1971). In the present scenario, the pseudogap emerges when the antiferromagnetic (AF) fluctuations (present in the Roth s band shift) become strongly sufficient to push down the region of the nodal point (π,π) on the renormalized quasi-particle bands. We observed that above a given total occupation nT , the specific heat decreases signaling the pseudogap presence. The effects of the antiferromagnetic fluctuations on the condensation energy and on superconductivity are also investigated.x

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Cluster dynamical mean field methods are used to calculate the superconductivity-induced changes in the interplane conductivity and Raman scattering cross section of the two-dimensional Hubbard model. When superconductivity emerges from the pseudogap, the superconducting response is found to be diminished in amplitude, broadened, and, in the case of the interplane conductivity, shifted to higher frequency. The results are in agreement with data on high-temperature copper-oxide superconductors indicating that the Hubbard model contains the essential low-energy physics of the pseudogap and its interplay with superconductivity in the cuprates.
Abstract The possibility of the superconducting transition in the repulsive Hubbard model on a square lattice is studied using the ladder approximation of the strong coupling diagram technique. The t – U and t – t ′– t ″– U models are considered in the regime of strong correlations, for the on-site Coulomb repulsion U = 8 t , in the range of temperatures 0.02 t ≲ T ≲ 0.3 t . To avoid the influence of the phase separation and size effects the calculations are performed in an infinite crystal, in the part of the phase diagram without inhomogeneities, for the electron concentration n ¯ = 0.92 . Solutions of the Eliashberg equation for singlet and triplet pairing, which are transformed according to one-dimensional representations of the lattice point group D 4 , are considered. For both models and all considered symmetries, eigenvalues of the Eliashberg equation are less than unity and demonstrate no upward trend with decreasing temperature. This result points to the absence of superconductivity in the Hubbard model in the strong-coupling regime. We discuss the reason for the small eigenvalue of the Eliashberg equation in the case of the singlet d x 2 − y 2 pairing.
The specific heat and the condensation energy of a two-dimensional Hubbard model, suitable to discuss high Tc superconductors (HTSTC), is studied taking into account hopping to first (t) and second (t2) nearest neighbors. Results for the Hubbard model show that the specific heat as a function of the temperature C(T) presents a two peaks structure (DUFFY; MOREO, 1997). The low temperature peak has been associated with spin fluctuation while the high temperature peak is related to charge fluctuation. Experimental results for the specific heat of HTSC s (LORAM et al., 2001), for instance, the YBCO and LSCO, indicate a close relation between the pseudogap and the specific heat. In the present work, we investigate the specific heat by the Green s function method within the n-pole approximation proposed by L. Roth (ROTH, 1969). The specific heat is calculated on the pseudogap and on the superconducting regions. Superconductivity with dx2−y2- wave pairing is considered following the procedure proposed by Beenen and Edwards (BEENEN; EDWARDS, 1995). The analytical expressions for the specific heat and for the condensation energy have been obtained following the formalism presented in reference (KISHORE; JOSHI, 1971). In the present scenario, the pseudogap emerges when the antiferromagnetic (AF) fluctuations (present in the Roth s band shift) become strongly sufficient to push down the region of the nodal point (π,π) on the renormalized quasi-particle bands. We observed that above a given total occupation nT , the specific heat decreases signaling the pseudogap presence. The effects of the antiferromagnetic fluctuations on the condensation energy and on superconductivity are also investigated.x