南京大学学报（自然科学版）2011，Vol.47Issue(2)：112-119,8.
S-P波混合超导的平均场理论谨以此文深切怀念敬爱的魏荣爵先生.他的关怀、支持和帮助,铭刻于心
Mean-field theory of S-P wave mixture superconductivity
摘要
Abstract
It has been well established that the mean field theory of the Hamiltonian for 4 fermions interaction system turns out to be expressed in terms of SU(2) (locally SO(3)) algebra for S-wave superconductivity, and SO (5) for P-wave superconductivity, whereas for the S-P wave mixture superconductivity is described by SU(4) (locally S0(6)) algebra. The P-wave superconductivity theories and their applications to liquid 3 He have intensively been studied in many early publications, which lead to a significant progress in the P-wave superconductivity. As we all know, S-wave superconductivity is the most fundamental phenomena of superconductivity, and the others are mostly appeared in the form of the mixture with the S-wave, such as the mixture of S-P wave in high temperature superconductivity. There have been more publications reported on the experimental studies of the coupling of S-P wave mixture superconductivity. Therefore, it is necessary to study the theory of the coupling of S-P wave mixture superconductivity.It is widely acknowledged that the core meaning of mean-field theory of the Hamiltonian is the consistency between the diagonalization of the Hamiltonian and the energy gap equation. The difficulty of mean-field theory for the S-P wave coupling is due to the involvement of a much bigger algebra (locally SU(4)), its diagonalization is not a easy thing. In this paper, it is mainly pointed out that the diagonalization of a SU(2) rotation which reflects the characteristics of SU(4), can diagonalized the Hamihonian, and set up the energy gap equation of 3-P wave mixture coupling. A subset of SU(4) containing only 6 generators, which describes the 3-P wave mixturesuperconductivity has been introduced into S0(6), so that the Hamiltonian of coherent state can be diagonalized.The energy gap equations for spin singlet and triplet are given. It is noted that the subset is formed in terms of the combination of three generators of SU(4) with spherical harmonic function Y1m (θ,φ) as coefficients, i.e. it still has more degrees of freedom. A special rotation of SU(2) in the subset of SU(4) and energy gap equation of the coupling of S-P wave mixture superconductivity related with diagonalized Hamiltonian are discussed, such as the reflection of S-P wave mixture on energy gap of the spin singlet and triplet states.关键词
S波/P波/S-P波混合/超导Key words
S-wave/ P-wave/ S-P mixture wave/ superconductor分类
数理科学引用本文复制引用
葛墨林,张宏标..S-P波混合超导的平均场理论谨以此文深切怀念敬爱的魏荣爵先生.他的关怀、支持和帮助,铭刻于心[J].南京大学学报（自然科学版）,2011,47(2):112-119,8.基金项目
国家自然科学基金(11075077) （11075077）
