Incorporation of charge- and pair-density-wave states into the one-band model of d-wave superconductivity
Michał Zegrodnik, Józef Spałek
DOI 10.1103/PhysRevB.98.155144 · Physical Review B
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Abstract
We study the coexistence of pair- (PDW) and charge-density-wave (CDW) states within the single-band t−J−U and Hubbard models of d-wave superconductivity and discuss our results in the context of the experimental observations for the copper-based compounds. In order to take the correlation effects into account with proper precision, we use the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF), which goes beyond the renormalized mean-field theory in a systematic manner. According to our analysis of the t−J−U model, the transition between the pure d-wave superconducting phase and the coexistent CDW+PDW phase takes place at δ≈0.18 (close to the optimal doping), with the modulated phase located in the underdoped regime. The situation is different for the case of the Hubbard model, where a narrow stability regime of a precursor nematic phase sets in preceding the formation of the modulated CDW+PDW state, with decreasing hole doping. The results conclude our comprehensive discussion of the standard phase diagram for high-TC superconducting compounds within the DE-GWF variational approach in the single narrow-band case [see J. Spałek et al., Phys. Rev. B 95, 024506 (2017); M. Zegrodnik and Spałek, Phys. Rev. B 95, 024507 (2017); Phys. Rev. B 96, 054511 (2017); New J. Phys. 20, 063015 (2018)].
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