A Phenomenological Theory Of Pairing Mechanism For Unconventional Superconductivity

Many unconventional superconductors exhibit multi-orbital and strong spin-orbit coupling characters,which induce various pairing symmetries and superconducting properties.Instead of electron-phonon coupling pairing glue in conventional supercon-ductors,quantum critical fluctuations are thought to be an important origin for uncon-ventional superconducting pairing.Realistic unconventional superconductors may be close to different quantum critical points,so multiple pairing interactions may coexist and contribute simultaneously to the superconductivity.It is therefore important to dis-cover and summarize the potential commonalities of unconventional superconductors in different kinds of systems for understanding the microscopic mechanism of unconven-tional superconductivity.This thesis constructs a phenomenological theoretical frame-work,which combines the Eliashberg theory and phenomenological multiple pairing interactions in unconventional superconductors,to understands the pairing mechanism of unconventional superconductors.As examples,we apply our framework to study monolayer Nb Se₂and Sr₂Ru O₄.Monolayer Nb Se₂is an Ising superconductor,and has unconventional properties such as extremely anisotropic upper critical field.Recent experiments found two-fold symmetry,or called nematicity,in the superconducting state,which breaks rotation symmetry of the crystal point group but is still lack of explanation.Monolayer Nb Se₂is found to be close to magnetic instability according to previous first-principles cal-culations.Here we consider electron-phonon coupling,ferromagnetic and antiferro-magnetic spin fluctuation interactions to study the possible pairing symmetry,based on our phenomenological framework.We find that the antiferromagnetic spin fluctua-tion can effectively suppress the superconducting state in A₁^′representation induced by electron-phonon coupling,and support the superconducting state in E^′representation,which has a(d_x2_-y2,d_xy)-wave-like gap function and breaks the rotation symmetry of the crystal point group.Our work provides a possible explanation of the nematicity in superconducting state of monolayer Nb Se₂.In 2019,a nuclear magnetic resonance experiment challenged the spin triplet p-wave pairing picture in Sr₂Ru O₄,which was soon verified by subsequent experiments.Ultrasound experiments suggested that Sr₂Ru O₄has a two-component superconducting order parameter,but its exact pairing symmetry is still under debate.Among all the possibilities,the accidentally degenerate d_x2_-y2+ig state seems to be the most promising candidate,which meets almost all experiments.However,how can g-wave emerge and become degenerate with d_x2_-y2-wave is still lack of reasonable theoretical explanations.To study possible pairing symmetry in Sr₂Ru O₄,we investigate the interplay of electric,antiferromagnetic and ferromagnetic multipole fluctuations as implied by previous experimental and theoretical studies,and explore the possible pairing symmetries,based on our phenomenological superconducting framework.We find that individual multipole fluctuation channels support s,d_x2_-y2or p-waves,but their interplay can lead to a large g-wave dominant region,which may yield the desired d_x2_-y2+ig state.Our study gives a possible theoretical basis for understanding the superconducting pairing symmetry of Sr₂Ru O₄.