Analyzing the success of T-matrix diagrammatic theories in representing a modified Hubbard model

We present a systematic study of various forms of renormalization that can be applied in the calculation of the self-energy of the Hubbard model within the T-matrix approximation. We compare the exact solutions of the attractive and repulsive Hubbard models, for linear chains of lengths up to eight sites, with all possible taxonomies of the T-matrix approximation. For the attractive Hubbard model, the success of a minimally self-consistent theory found earlier in the atomic limit (Phys. Rev. B 71, 155111 (2005)) is not maintained for finite clusters unless one is in the very strong correlation limit. For the repulsive model, in the weak correlation limit at low electronic densities -- that is, where one would expect a self-consistent T-matrix theory to be adequate -- we find the fully renormalized theory to be most successful. In our studies we employ a modified Hubbard interaction that eliminates all Hartree diagrams, an idea which was proposed earlier (Phys. Rev. B 63, 035104 (2000)).Comment: Includes modified discussion of 1st-order phase transition. Accepted for publication in J. Phys.: Condensed Matte

Evidence for precursor superconducting pairing above T c in underdoped cuprates from an analysis of the in-plane infrared response

We performed calculations of the in-plane infrared response of underdoped cuprate superconductors to clarify the origin of a characteristic dip feature which occurs in the published experimental spectra of the real part of the in-plane conductivity below an onset temperature ${{T}^{{\rm ons}}}$ considerably higher than ${{T}_{{\rm c}}}$. We provide several arguments, based on a detailed comparison of our results with the published experimental data, confirming that the dip feature and the related features of the memory function $M(\omega )={{M}_{1}}(\omega )+{\rm i}{{M}_{2}}(\omega )$ (a peak in M1 and a kink in M2) are due to superconducting pairing correlations that develop below ${{T}^{{\rm ons}}}$. In particular, we show that (i) the dip feature, the peak and the kink of the low-temperature experimental data can be almost quantitatively reproduced by calculations based on a model of a d-wave superconductor. The formation of the dip feature in the experimental data below ${{T}^{{\rm ons}}}$ is shown to be analogous to the one occurring in the model spetra below ${{T}_{{\rm c}}}$. (ii) Calculations based on simple models, for which the dip in the temperature range from ${{T}_{{\rm c}}}$ to ${{T}^{{\rm ons}}}$ is unrelated to superconducting pairing, predict a shift of the onset of the dip at the high-energy side upon entering the superconducting state, that is not observed in the experimental data; (iii) the conductivity data in conjunction with the recent photoemission data (Reber et al 2012 Nat. Phys. 8 606, Reber et al 2013 Phys. Rev. B 87 060506) imply the persistence of the coherence factor characteristic of superconducting pairing correlations in a range of temperatures above ${{T}_{{\rm c}}}$

Stability of condensate in superconductors

According to the BCS theory the superconducting condensate develops in a single quantum mode and no Cooper pairs out of the condensate are assumed. Here we discuss a mechanism by which the successful mode inhibits condensation in neighboring modes and suppresses a creation of noncondensed Cooper pairs. It is shown that condensed and noncondensed Cooper pairs are separated by an energy gap which is smaller than the superconducting gap but large enough to prevent nucleation in all other modes and to eliminate effects of noncondensed Cooper pairs on properties of superconductors. Our result thus justifies basic assumptions of the BCS theory and confirms that the BCS condensate is stable with respect to two-particle excitations