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Model-mapped RPA to evaluate superconductivity in FLEX from first-principles

Hirofumi Sakakibara, Takao Kotani

Published Dec 10, 2018• 0 citations
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Abstract

We have applied the model-mapped RPA [H. Sakakibara et al., J. Phys. Soc. Jpn. 86, 044714 (2017)] to the cuprate superconductors La2CuO4 and HgBa2CuO4, resulting two-orbital Hubbard models. All the model parameters are determined based on first-principles calculations. For the model Hamiltonians, we perform fluctuation exchange calculation. Results are consistent with experimental Tc. In addition, we give some analyses for the interaction terms in the model, especially comparisons with those of the constrained RPA.

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We have applied the model-mapped RPA [H. Sakakibara et al., J. Phys. Soc. Jpn. 86, 044714 (2017)] to the cuprate superconductors La2CuO4 and HgBa2CuO4, resulting two-orbital Hubbard models. All the model parameters are determined based on first-principles calculations. For the model Hamiltonians, we perform fluctuation exchange calculation. Results are consistent with experimental Tc. In addition, we give some analyses for the interaction terms in the model, especially comparisons with those of the constrained RPA.
We have applied the model-mapped random phase approximation (RPA) [H. Sakakibara et al., J. Phys. Soc. Jpn. 86, 044714 (2017)] to the cuprate superconductors La2CuO4{\mathrm{La}}_{2}{\mathrm{CuO}}_{4}La2​CuO4​ and HgBa2CuO4{\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4}HgBa2​CuO4​, resulting in two-orbital Hubbard models. All the model parameters are determined based on first-principles calculations. For the model Hamiltonians, we perform fluctuation exchange calculation. Results explain relative height of Tc{T}_{c}Tc​ observed in experiment for La2CuO4{\mathrm{La}}_{2}{\mathrm{CuO}}_{4}La2​CuO4​ and HgBa2CuO4{\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4}HgBa2​CuO4​. In addition, we give some analyses for the interaction terms in the model, especially comparisons with those of the constrained RPA.
We present a new method to obtain interaction part of a model Hamiltonian from the result of the first-principles calculation. The effective interaction contained in the model is determined based on the random phase approximation (RPA). In contrast to previous methods such as projected RPA or constrained RPA, the new method takes into account the long-range part of the polarization effect when determining the interaction in the model. After we discuss problems in previous RPA methods, we will give the formulation of the new method, and show how it works for the single-band Hubbard model of HgBa2_22​CuO4_44​.
Spin-only descriptions of the half-filled one-band Hubbard model are relevant for a wide range of Mott insulators. In addition to the usual Heisenberg exchange, many other types of interactions, including ring exchange, appear in the effective Hamiltonian in the intermediate coupling regime. In order to improve on the quantitative description of magnetic excitations in the insulating antiferromagnetic phase of copper-oxide (cuprate) materials, and to be consistent with band-structure calculations and photoemission experiments on these systems, we include second- and third-neighbor hopping parameters, ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, into the Hubbard Hamiltonian. A unitary transformation method is used to find systematically the effective Hamiltonian and any operator in the spin-only representation. The results include all closed four-hop electronic pathways in the canonical transformation. The method generates many ring exchange terms that play an important role in the comparison with experiments on La2CuO4{\text{La}}_{2}{\text{CuO}}_{4}La2​CuO4​. Performing a spin-wave analysis, we calculate the magnon dispersion as a function of UUU, ttt, ${t}^{\ensuremath{'}}$, and ${t}^{\ensuremath{''}}$. The four parameters are estimated by fitting the magnon dispersion to the experimental results of Coldea et al. [Phys. Rev. Lett. 86, 5377 (2001)] for La2CuO4{\text{La}}_{2}{\text{CuO}}_{4}La2​CuO4​. The ring exchange terms are found essential, in particular to determine the relative sign of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, with the values found in good agreement with independent theoretical and experimental estimates for other members of the cuprate family. The zero-temperature sublattice magnetization is calculated using these parameters and also found to be in good agreement with the experimental value estimated by Lee et al. [Phys. Rev. B 60, 3643 (1999)]. We find a value of the interaction strength $U\ensuremath{\simeq}8t$ consistent with Mott insulating behavior.
We present an algorithm for microscopic modeling of superconducting states of arbitrary pairing symmetry via an implementation of self-consistent perturbation theory, the fluctuation exchange approximation (FLEX), applied to Hubbard-like models. Like the original formulation of FLEX, all ring diagrams that are generated with the bare interaction vertex are included in the generating functional for the self-energy. Thus, this algorithm is suitable for FLEX-based Hubbard model calculations in both the attractive and repulsive cases.
We study the emergence of superconductivity in the one-band Hubbard model using the spin-rotation-invariant Kotliar-Ruckenstein slave-boson (SB) approach. Motivated by its intrinsically renormalized mean-field ground state, we construct an effective pairing vertex from dynamical fluctuations about the saddle point. Solving the anisotropic, frequency-dependent gap equation on the square lattice, we map the pairing instabilities across doping, interaction, temperature and real-frequency gap structure that qualitatively match experimental cuprate observations. This framework merges strong-correlation SB-type renormalizations with RPA-type pairing transparency, providing a scalable route to modeling multi-orbital superconductivity at strong coupling.
The relationship between crystal structures and superconducting critical temperatures has attracted considerable attention as a clue to designing higher-TcT_{\rm c}Tc​ superconductors. In particular, the relationship between the number nnn of CuO2_22​ layers in a unit cell of cuprate superconductors and the optimum superconducting transition temperature TcoptT_{\rm c}^{\rm opt}Tcopt​ is intriguing. As experimentally observed in layered cuprates, TcoptT_{\rm c}^{\rm opt}Tcopt​ increases when nnn is increased, up to n=3n=3n=3, and, then, decreases for larger nnn. However, the mechanism behind the nnn dependence of TcoptT_{\rm c}^{\rm opt}Tcopt​ remains elusive although there have been many studies on the nnn dependence. In this paper, we studied a bilayer ttt-t′t't′ Hubbard model to clarify the effects of the adjacent CuO2_22​ layers on the stability of the superconductivity by using a many-variable variational Monte Carlo method. We calculate the superconducting correlation at long distance and zero temperature, and the amplitude of the superconducting gap functions estimated from the momentum distribution as the observables correlated with TcoptT_{\rm c}^{\rm opt}Tcopt​. It is found that the in-plane superconducting correlation is not enhanced in comparison with that in the single-layer ttt-t′t't′ Hubbard model. The superconducting correlations of the bilayer Hamiltonian are significantly small in the overdoped region in comparison with those of single-layer Hamiltonian, which is attributed to the van Hove singularity. In addition, we found that the amplitude of the superconducting gap functions is also similar in both the single-layer and bilayer ttt-t′t't′ Hubbard model at the optimal doping. Therefore, we conclude that the adjacent Hubbard layers are not relevant to the enhancement of TcoptT_{\rm c}^{\rm opt}Tcopt​ in the bilayer cuprates. Possible origins of the enhanced TcoptT_{\rm c}^{\rm opt}Tcopt​ other than the adjacent layers are also discussed.