Study On The Microscopic Mechanism Of Iron-based And Topological Superconductors

The pairing symmetry and pairing mechanism are the two basic questions for the stud-ies of superconductivity. For conventional BCS-type superconductors, it’s the phonon that mediates pairing and the pairing gap is conventional s-wave like. However there are a lot of the superconductors that can not be described by the conventional BCS theory, constituting the family of unconventional superconductors. They mainly in-clude heave-fermion superconductors, organic superconductors, cuprate superconduc-tors, iron-based superconductors and the neutral-version Helium-3superfluids. They are unconventional in many aspects such as high superconducting transition tempera-ture beyond the McMillan limit in some systems, strong-correlation effects, close rela-tion to magnetism, pairing symmetries beyond the conventional s-wave, etc. Although there is no consensus on the pairing mechanism for the unconventional superconduc-tors, majority of the community believe that it’s the antiferromagnetic spin fluctuation that is responsible for most unconventional superconductors such as cuprates and iron-based superconductors. From the theoretical point of view, the interaction enhanced in the magnetic channel due to Coulomb interaction will induce effective pairing in-teraction. As long as the magnetic interaction is not strong enough to form magnetic order, superconductivity will emerge in low energy scale due to Cooper instability. The wavevector of the antiferromagnetic spin fluctuation (QSF) is mainly determined by the nesting structure of the Fermi surface, although in some cases high energy particle-hole scattering can be predominant. For the former case, the pairing gaps on the fermi sur-face sections connected by QSF will change sign, forming unconventional even-parity pairing symmetry, e.g. d-wave for some heavy-fermion superconductors and cuprates, s±wave for iron-pnictides, etc. For the later case, the pairing symmetry depends on the competition between the high-energy and low-energy freedom of the system such as alkaline iron-selenide superconductors.The recently found topological insulators have opened a new direction in the con-densed matter community and lots of successes have been achieved. However the superconducting version, i.e. topological superconductors are still an open issue. Es-pecially, study on the correlation induced intrinsic time-reversal invariant topological superconductor is still in its early stage on both experimental and theoretical sides. Phenomenological studies have shown that the some special type of p-wave pairing is topological nontrivial and supports Majorana fermions on the boundary. In spin space the p-wave pairing corresponds to spin-triplet pairing. By analogy to the spin-singlet pairing case, the ferromagnetic fluctuation may induce p-wave pairing.In this dissertation, we utilize the singular-mode functional renormalization group method to study the pairing symmetries and pairing mechanisms in unconventional su-perconductors. We have systematically investigated the properties of iron-based super-conductors with spin-singlet pairing and a case of spin-triplet pairing in correlation-induced topological superconductors. All the results point to a conclusion that the pairing in these systems may be mediated by the spin-fluctuation and the pairing sym-metry is closely related to the type of spin-fluctuation. The main text is organized as follows.In Chap. I, we introduce the idea of pairing and shortly discuss the pairing sym-metry and pairing mechanism in unconventional superconductors. We then summarize the existing theoretical methods and give a short introduction to our singular-mode functional renormalization group method.In Chap. Ⅱ, we mainly talk about the pairing in iron pnictides, the most common family of iron-based superconductors. We show that for both the minimal two-orbital model and the complete five-orbital model the pairing symmetry is s±wave. The com-parison between the two model shows that the dxy orbit is also important suggesting that it may not be neglected for more detailed studies.In Chap. Ⅲ, we study the pairing in recently found alkaline iron-selenide super-conductors. We show that the high-energy particle-hole scatterings are predominant in these materials. The hybridization effect is important which will tip the pairing sym-metry from d-wave to s-wave with no sign-change of the pairing gap function on the two fermi surface.In Chap. IV, we study the effect of electron-phonon interaction in cuprates and the monolayer FeSe superconductor. For cuprates, we find that only the Big phonon will enhance the superconducting divergent scale. For the monolayer FeSe, when the gaps on the two pockets are of the same sign, phonons of the substrate will significantly enhance the superconducting transition temperature.In Chap. V, we compare the results for the itinerant picture and the local-moment picture. We find that the two pictures are qualitatively consistent with each other. Concerning the case of alkaline iron-selenide superconductors, its pairing symmetry is s-wave in both pictures.In Chap. VI, we consider the pairing mechanism of topological superconduc-tors induced by strong correlation. Through spin-resolved SMFRG we find that the ferromagnetic fluctuation or small-wavevector spin fluctuation will induce degenerate p-wave pairing and a small Rashba spin-orbit coupling will drive them to form time-reversal invariant topological pairing.In Chap. VII we shortly summarize this dissertation and in the Appendix we show the derivation of the Eliashberg equation.