Effects Of Spin-orbit Coupling On The Co-existence Model Of Mixed Superconductivity And Ferromagnetism

Superconductivity is one of the most important phenomena in condensed matter physics.The isotropic s-wave superconductivity is based on the electron-phonon coupling mechanism,and its microscopic mechanism has been perfectly interpreted by the BCS theory.However,the conventional BCS theory has certain limitations,it is diff-icult to reveal the superconductivity of unconventional superconductors,and further theoretical research is needed.At the same time,some unconventional superconductors exhibit rich and strange physical phenomena due to the existence of spin-orbit coupling effects,such as mixed parity,topological insulation state,and Anti-constant spin Hall effect.In order to further investigate the effect of spin-orbit coupling on unconventional superconductivity,the symmetry of the superconducting pair and the superconducting low-temperature characteristics of Rashba and Dresslhaus under the co-existence of two types of spin-orbit coupling were studied by algebraic method.The main research contents and conclusions are as follows:(1)Firstly,we establish a two-dimensional(s+p)-wave mixed superconductivity and ferromagnetic coexistence model with spin-orbit coupling.Based on the principle of SO(5)symmetry,the Hamiltonian of the system under the mean field approximation is expressed by SO(5)Lie algebra as a ten-dimensional linear structure.And then,the corresponding coherent state operator is introduced to diagonalize the Hamiltonian by unitary transformation,the quasiparticle excitation spectrum,the eigenvalues and eigenstates of the mixed system are derived.(2)Secondly,we use the Bogoliubov transformation to establish a self-consistent superconductivity gap equation and discuss several cases.The results show that under the influence of spin-orbit coupling and Zeeman effect,when there is only s-wave pairing potential,the superconductivity gap function appears as a spin-singlet s-wave superconductivity coexisting with ferromagnetic.When there is only a p-wave pairing potential,the superconductivity gap function appears as a spin-triplet p-wave superconductivity coexists with ferromagnetism.Finally,when the s-wave and p-wave pairing potentials coexist,the superconductivity gap function appears as a spin-singlet s-wave and spin-triplet p-wave mixed superconductivity and ferromagnetism coexist.However,when the spin-orbit coupling interaction does not exist,the spin-triplet pairing disappears,and the superconducting energy gap function appears as a single-band s-wave pairing.(3)Finally,we use the density of superconducting quasi-particle states and low-temperature electron specific heat to analyze and judge the superconducting energy gap topology and its pairing symmetry.The results show that under the influence of spin-orbit coupling and Zeeman effect,the superconducting quasi-particle bands split.The superconducting gap is not topologically stable and is modulated by the Zeeman field when there is only s-wave pairing potential.When ?B<As,spin-orbit coupling and Zeeman effect can induce no-node waves.When ?_BB ??,the contribution of superconductivity mainly comes from hole-type Fermi surface,forming a nodal s-wave superconductivity.When there is only p-wave pairing potential,the superconducting energy gap has a stable line node and appears as a spin-triplet p-wave pairing.For the mixed pairing potential of(s+p)-wave,the topological structure of the superconducting energy gap is also modulated by the Zeeman field,and the gap node cannot exist stably.Under the condition of ?B<?s,a gap appears in the superconducting energy gap,and the superconducting pairing is dominated by spin-singlet pairing.Under the condition of ?_BB??s,Zeeman field can inhibit the superconductivity of spin-singlet pairing,so that the superconducting energy gap appears nodes,and the superconducting pairing method is mainly spin-triplet pairing.In addition,under the influence of no spin-orbit coupling interaction and Zeeman effect,the superconducting energy gap will be fully gapped and behave as isotropic s-wave superconductivity.