Plain s-Wave Superconductivity near Magnetic Criticality: Enhancement of Attractive Electron–Boson Coupling Vertex Corrections

Abstract

Recent experiments revealed that the plain s-wave state without any sign-reversal emerges in various metals near magnetic criticality. To understand this counter-intuitive phenomenon, we study the gap equation for the multiorbital Hubbard-Holstein model, by analyzing the vertex correction (VC) due to the higher-order electron-correlation effects. We find that the phonon-mediated orbital fluctuations are magnified by the VC for the susceptibility (χ-VC). In addition, the charge-channel attractive interaction is enlarged by the VC for the coupling-constant (U -VC), which is significant when the interaction has prominent q-dependences; therefore the Migdal theorem fails. Due to both χ-VC and U -VC, the plain s-wave state is caused by the small electron-phonon interaction near the magnetic criticality against the repulsive Coulomb interaction. We find that the direct Coulomb repulsion for the plain s-wave Cooper pair is strongly reduced by the "multiorbital screening effect." Keywords: orbital fluctuations, self-consistent vertex correction theory, magnetic quantum criticality It is widely believed that the spin-fluctuations are harmful for the conventional s-wave superconductivity. However, recent experiments have revealed that the plain s-wave state without any sign-reversal emerges in some strongly-correlated metals near the magnetic instability. For example, plain s-wave superconductivity with high T c is reported in heavily electron-doped FeSe families (T c = 60 ∼ 100K) [1, 2] and in A 3 C 60 (A =K, Rb, Cs; T c > 30K) [3]. In both compounds, electron-phonon (e-ph) interaction may play a crucial role in the pairing mechanism, as discussed in Refs. [4][5][6][7][8][9][10]. Even so, a fundamental question is why the high-T c plain s-wave state appears against the repulsive interaction by spinfluctuations. More surprisingly, the plain s-wave state is reported in heavy-fermion superconductor CeCu 2 Si 2 near the magnetic phase, according to the measurements of the specific heat, penetration depth, thermal conductivity, and electron irradiation effect on T c [11,12].Therefore, it is a significant problem for theorists to establish a general mechanism of the plain s-wave superconductivity in strongly correlated electron systems. One important feature of these s-wave superconductors would be the orbital degrees of freedom. In this case, in principle, the pairing glue for the plain s-wave state may be realized by the orbital fluctuations. The two possible origins of the orbital fluctuations are the higherorder many-body process given by the vertex correction (VC) [13] and the e-ph interaction [14]. The significant questions are (i) whether these two different origins of the orbital fluctuations (i.e., the VC due to Coulomb interaction and the e-ph interaction) cooperate or not, (ii) why the high-T c plain s-wave state is realized against the strong magnetic fluctuations, and (iii) how the plain swave Cooper pairs escape from the strong direct Coulomb repulsion in multiorbital systems.In this paper, we analyze a canonica...

Fully gapped s -wave superconductivity enhanced by magnetic criticality in heavy-fermion systems

“…This is qualitatively similar to d-electron systems without SOI as shown in Fig.2(c) in Ref. [35]. In conclusion, U -VC in f -electron systems give significant contribution as well as in d-electron systems.…”

“…We revealed that s-wave superconductivity is strongly enhanced near the magnetic criticality in multi-orbital heavy fermion systems, once moderate phonon-induced multipole fluctuations exist as shown in Fig.6. Note that the depairing effect of Coulomb interaction is reduced by the multiorbital screening effect [35]. The present mechanism may be responsible for the fully gapped s-wave superconducting state realized in CeCu 2 Si 2 .…”

“…For finite g,Î c (∝χ c ) develops as large asÎ s andÎ s⊥ . We put g = 0 forΛ ch approximately since the contribution from χ c remains small even for g > 0 [35]. Figures 6(a)-(b) are obtained phase diagrams, which show the largest eigenvalue and its symmetry of the gap function.…”

Multipole fluctuation theory for heavy fermion systems: Application to multipole orders in CeB6

“…In HF systems, phonon-mediated superconductivity can be stabilized by the AL-process for the electron-boson coupling. This mechanism may be responsible for the fully gapped s-wave state in CeCu 2 Si 2 [26,37]. These findings indicate that the AL-VC plays essential roles in HF systems…”

Full-Gap Superconductivity Robust against Disorder in Heavy-Fermion CeCu2Si2

“…The s þþ -wave state inferred in this study is generally a manifestation of on-site attractive interactions, but how this can overcome the strong Coulomb repulsion in such a strongly correlated electron system calls for new theoretical approaches beyond the widespread spin-fluctuation-based unconventional mechanism of superconductivity. Very recent calculations show that in the vicinity of magnetic quantum critical point, the orbital fluctuations may lead to s þþ -wave superconductivity [32]. Indeed, the importance of orbital degrees of freedom has been pointed out in several aspects for some Ce-based materials including CeM 2 Si 2 , where M is a transition metal element [33][34][35].…”