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

作　　者：葛墨林[1] 张宏标[2] 

机构地区：[1]南开大学陈省身数学所理论物理室,天津300071 [2]东北师范大学物理系,长春130024

出　　处：《南京大学学报（自然科学版）》2011年第2期112-119,共8页Journal of Nanjing University（Natural Science）

基　　金：国家自然科学基金(11075077)

摘　　要：对于由4个费米子相互作用系统组成的哈密顿量的平均场理论,当只有S波超导时,由SU(2)(局域同构于SO(3))代数表达,P波超导可以通过SO(5)表达,而对于S-P混合波超导的情况则由SU(4)(局域同构于SO(6))代数表达.本文通过在SO(6)代数中引入了反映S波和P波混合超导的SO(4)子集,从而可以通过对相干态算子的对角化,给出与自旋单态和自旋三重态相对应的能隙方程.值得注意的是,这个SO(4)子集仍然具有相当大的自由度,其中还包含以球谐函数Ylm(θ,φ)为系数的一些SU(4)生成元的组合项.并讨论了SU(4)子集里一个特定SU(2)旋的与对角化相对应的S-P混合波超导耦合的超导能隙方程,例如S-P波混合对自旋单态和三重态能隙的影响等.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 SO(6)) algebra.The P-wave superconductivity theories and their applications to liquid 3He 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 Hamiltonian,and set up the energy gap equation of S-P wave mixture coupling.A subset of SU(4) containing only 6 generators,which describes the S-P wave mixture superconductivity has been introduced into SO(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,) as coefficients,i.e.it still has more degrees of freedom.A specia

关 键 词：S波 P波 S-P波混合 超导 

分 类 号：O511[理学—低温物理]