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Register a new userStrongly enhanced superconductivity due to finite energy spin fluctuations induced by an incipient band : a FLEX study on the bilayer Hubbard model with vertical and diagonal interlayer hoppings
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We study the spin-fluctuation-mediated $spm$-wave superconductivity in the bilayer Hubbard model with vertical and diagonal interlayer hoppings. As in the two-leg ladder model with diagonal hoppings, studied previously by the present authors, superconductivity is strongly enhanced when one of the bands lies just below (or touches) the Fermi level, that is, when the band is incipient. The strong enhancement of superconductivity is because large weight of the spin fluctuations lies in an appropriate energy range, whereas the low energy, pair-breaking spin fluctuations are suppressed. The optimized eigenvalue of the linearized Eliashberg equation, a measure for the strength of superconductivity, is not strongly affected by the bare width of the incipient band, but the parameter regime where superconductivity is optimized is wide when the incipient band is narrow, and in this sense, the coexistence of narrow and wide bands is favorable for superconductivity.
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The nature and mechanism of superconductivity in the extremely electron-doped FeSe based superconductors continues to be a matter of debate. In these systems, the hole-like band has moved below the Fermi energy, and various spin-fluctuation theories involving pairing between states near the electron Fermi surface and states of this incipient band have been proposed. Here, using a dynamic cluster quantum Monte Carlo calculation for a bilayer Hubbard model we show that the pairing in these systems can be understood in terms of an effective retarded attractive interaction between electrons near the electron Fermi surface.
The weak-coupling renormalization group method is an asymptotically exact method to find superconducting instabilities of a lattice model of correlated electrons. Here we extend it to spin-orbit coupled lattice systems and study the emerging superconducting phases of the Rashba-Hubbard model. Since Rashba type spin-orbit coupling breaks inversion symmetry, the arising superconducting phases may be a mixture of spin-singlet and spin-triplet states. We study the two-dimensional square lattice as a paradigm and discuss the symmetry properties of the arising spin-orbit coupled superconducting states including helical spin-triplet superconductivity. We also discuss how to best deal with split energy bands within a method which restricts paired electrons to momenta on the Fermi surface.
Identification of pairing mechanisms leading to the unconventional superconductivity realized in copper-oxide, heavy-fermions, and organic compounds is one of the most challenging issues in condensed-matter physics. Clear evidence for an electron-phonon mechanism in conventional superconductors is seen by the isotope effect on the superconducting transition temperatures $T_{rm SC}$, since isotopic substitution varies the phonon frequency without affecting the electronic states. In unconventional superconductors, magnetic fluctuations have been proposed to mediate superconductivity, and considerable efforts have been made to unravel relationships between normal-state magnetic fluctuations and superconductivity. Here, we show that characteristic experimental results on the ferromagnetic (FM) superconductor UCoGe ($T_{rm Curie} sim 2.5 $ K and $T_{rm SC} sim 0.6$ K) can be understood consistently within a scenario of the spin-triplet superconductivity induced by FM spin fluctuations. Temperature and angle dependencies of the upper critical magnetic field of the superconductivity ($H_{c2}$) are calculated on the basis of the above scenario by solving the Eliashberg equation. Calculated $H_{c2}$ well agrees with the characteristic experimental results observed in UCoGe. This is a first example that FM fluctuations are shown to be a pairing glue of superconductivity.
Here we have developed a FLEX+DMFT formalism, where the symmetry properties of the system are incorporated by constructing a SO(4) generalization of the conventional fluctuation-exchange approximation (FLEX) coupled self-consistently to the dynamical mean-field theory (DMFT). Along with this line, we emphasize that the SO(4) symmetry is the lowest group-symmetry that enables us to investigate superconductivity and antiferromagnetism on an equal footing. We have imposed this by decomposing the electron operator into auxiliary fermionic and slave-boson constituents that respect SU(2)$_{rm spin}otimes$SU(2)$_{eta{rm spin}}$. This is used not in a mean-field treatment as in the usual slave-boson formalisms, but instead in the DMFT impurity solver with an SU(2)$_{rm spin}otimes$SU(2)$_{eta{rm spin}}$ hybridization function to incorporate the FLEX-generated bath information into DMFT iterations. While there have been attempts such as the doublon-less SU(2) slave-boson formalism, the present full-SU(2) slave-boson formalism is expected to provide a new platform for addressing the underlying physics for various quantum orders, which compete with each other and can coexist.
The dynamical mean-field theory (DMFT) combined with the fluctuation exchange (FLEX) method, namely FLEX+DMFT, is an approach for correlated electron systems to incorporate both local and non-local long-range correlations in a self-consistent manner. We formulate FLEX+DMFT in a systematic way starting from a Luttinger-Ward functional, and apply it to study the $d$-wave superconductivity in the two-dimensional repulsive Hubbard model. The critical temperature ($T_c$) curve obtained in the FLEX+DMFT exhibits a dome structure as a function of the filling, which has not been clearly observed in the FLEX approach alone. We trace back the origin of the dome to the local vertex correction from DMFT that renders a filling dependence in the FLEX self-energy. We compare the results with those of GW+DMFT, where the $T_c$-dome structure is qualitatively reproduced due to the same vertex correction effect, but a crucial difference from FLEX+DMFT is that $T_c$ is always estimated below the N{e}el temperature in GW+DMFT. The single-particle spectral function obtained with FLEX+DMFT exhibits a double-peak structure as a precursor of the Hubbard bands at temperature above $T_c$.
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