非常规超导体中FFLO态、自旋涨落与超导配对对称性的理论研究
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摘要
本文分为以下三个主要部分：
第一部分,我们首先介绍了区别于普通BCS配对的FFLO超导态。由于有着严格的条件限制,目前还没有很好的实验可以来展示FFLO态的出现。在各向异性的三角晶格上通过自洽求解Bogoliubov-de Gennes (BdG)方程,我们研究了磁阻挫与出现FFLO态之间的关联。计算结果表明进入FFLO态所需的最小磁场(下临界磁场)随着各向异性比例系数t2/t1的增大而单调递减,下临界磁场也随着库伦排斥作用U的增大而降低。另外也发现了在杂质的影响下,FFLO态在大的各向异性比例系数条件下更加稳定。以上几点都同时表明磁阻挫的存在将会大大有助于进入FFLO态。因此我们指出有着磁阻挫结构或在适当的静态液压下的层状有机超导体将会有利于FFLO态的形成,这一理论研究也为今后寻找FFLO态的实验工作给出了建议和参考。
第二部分,通过分别选取s±-波,s-波以及d-波三种不同配对对称性,自洽地求解两带模型的BdG方程,我们研究了磁场与非磁杂质对近年来新发现的铁基超导体的态密度以及自旋晶格弛豫率T1-1的影响。结果显示态密度的线形特征与配对对称性有很大的依赖关系,随着温度的降低在Tc以下三种配对的弛豫率在磁场的影响下大体都呈现了从T1-1～T3到T线性关系的转变,当引入杂质后,s±-波与d-波的弛豫率随温度的依赖关系较为相似,而杂质对s-波则几乎没有影响。我们的研究指出在磁场或者非磁杂质影响的情况下不易区分铁基超导体的s士-波和d-波超导配对对称性。
第三部分,我们利用五轨道模型研究了新型电子型铁基超导材料KyFe2-xSe2中的自旋涨落、能带的重整化效应和超导配对对称性,发现由于自旋涨落引起的超导配对对称性有可能是dx2-y2波配对,并且详细研究了相互作用强度和掺杂浓度对自旋涨落和超导配对对称性的影响。另外在实空间格点上考虑有序铁空位对该超导材料性质的影响,运用t-J1-J2-J3模型,通过自洽求解BdG方程,得到了在不同磁交换相互作用下磁有序分布的情况。并获得了在该系统中与实验相一致的小集团星棋盘反铁磁分布态(blocked checkerboard AFM).
This paper is organized as follows:
In section I, we introduce the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) un-conventional superconductors firstly. Because an unambiguous experimental demon-stration of the FFLO state is hindered by the stringent requirements for its realization. Based on the theories of the mean-field by self-consistently solving Bogoliubov-de Gennes(BdG) equations, we study theoretically the relationship between the magnetic frustration and the emergence of the FFLO state on a triangular lattice. We find that the required lower critical magnetic field to enter the FFLO state decreases with the increase of both the anisotropic ratio and the on-site Coulomb repulsive interaction and at the effect of impurities, the FFLO state is stable at a large anisotropic ratio. These results demonstrate that it is easier to enter the FFLO state on the structurally frustrated triangular lattice in comparison with the square lattice, and suggest that the layered or-ganic superconductors with a triangular lattice and/or under an appropriate hydrostatic pressure may be good candidates for exploring the FFLO state.
In section II, the effects of magnetic vortices and nonmagnetic impurities on the low energy quasiparticle excitations and the spin-lattice relaxation rate are examined in the iron-based superconductors for the s±-, s-and d-wave pairing symmetries, respec-tively. The main effect of the vortices is to enhance the quasiparticle excitations and the spin-lattice relaxation rate for all symmetries, and leads to a T3dependence of the re-laxation rate followed by a nearly T-linearity at lower temperatures. This enhancement can only be seen for the s±-and d-wave symmetries in the presence of nonmagnetic impurities. These results suggest that the s±-wave and d-wave pairing states behave similarly in response to the magnetic field and nonmagnetic impurities, therefore it may be impossible to distinguish them on the basis of the measurements of spin-lattice relaxation rates when a magnetic field and/or impurity scatterings are present.
In section Ⅲ, we investigate the band renormalization, FS reconstruction and the symmetry of the superconducting gap in KyFe2-xSe2iron-based superconductors using a five-orbital model. We have found that the most favorable superconducting pairing symmetry mediated by the spin fluctuations is the dx2-y2-wave. By using the t-J1-J2-J3model, we have studied the distribution of the magnetic order in this system in the presence of the Fe vacancies. We have also analyzed the magnetic phase diagram and find a blocked checkerboard antiferromagnetic order in agreement with the experimental measurements.
第一部分,我们首先介绍了区别于普通BCS配对的FFLO超导态。由于有着严格的条件限制,目前还没有很好的实验可以来展示FFLO态的出现。在各向异性的三角晶格上通过自洽求解Bogoliubov-de Gennes (BdG)方程,我们研究了磁阻挫与出现FFLO态之间的关联。计算结果表明进入FFLO态所需的最小磁场(下临界磁场)随着各向异性比例系数t2/t1的增大而单调递减,下临界磁场也随着库伦排斥作用U的增大而降低。另外也发现了在杂质的影响下,FFLO态在大的各向异性比例系数条件下更加稳定。以上几点都同时表明磁阻挫的存在将会大大有助于进入FFLO态。因此我们指出有着磁阻挫结构或在适当的静态液压下的层状有机超导体将会有利于FFLO态的形成,这一理论研究也为今后寻找FFLO态的实验工作给出了建议和参考。
第二部分,通过分别选取s±-波,s-波以及d-波三种不同配对对称性,自洽地求解两带模型的BdG方程,我们研究了磁场与非磁杂质对近年来新发现的铁基超导体的态密度以及自旋晶格弛豫率T1-1的影响。结果显示态密度的线形特征与配对对称性有很大的依赖关系,随着温度的降低在Tc以下三种配对的弛豫率在磁场的影响下大体都呈现了从T1-1～T3到T线性关系的转变,当引入杂质后,s±-波与d-波的弛豫率随温度的依赖关系较为相似,而杂质对s-波则几乎没有影响。我们的研究指出在磁场或者非磁杂质影响的情况下不易区分铁基超导体的s士-波和d-波超导配对对称性。
第三部分,我们利用五轨道模型研究了新型电子型铁基超导材料KyFe2-xSe2中的自旋涨落、能带的重整化效应和超导配对对称性,发现由于自旋涨落引起的超导配对对称性有可能是dx2-y2波配对,并且详细研究了相互作用强度和掺杂浓度对自旋涨落和超导配对对称性的影响。另外在实空间格点上考虑有序铁空位对该超导材料性质的影响,运用t-J1-J2-J3模型,通过自洽求解BdG方程,得到了在不同磁交换相互作用下磁有序分布的情况。并获得了在该系统中与实验相一致的小集团星棋盘反铁磁分布态(blocked checkerboard AFM).
This paper is organized as follows:
In section I, we introduce the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) un-conventional superconductors firstly. Because an unambiguous experimental demon-stration of the FFLO state is hindered by the stringent requirements for its realization. Based on the theories of the mean-field by self-consistently solving Bogoliubov-de Gennes(BdG) equations, we study theoretically the relationship between the magnetic frustration and the emergence of the FFLO state on a triangular lattice. We find that the required lower critical magnetic field to enter the FFLO state decreases with the increase of both the anisotropic ratio and the on-site Coulomb repulsive interaction and at the effect of impurities, the FFLO state is stable at a large anisotropic ratio. These results demonstrate that it is easier to enter the FFLO state on the structurally frustrated triangular lattice in comparison with the square lattice, and suggest that the layered or-ganic superconductors with a triangular lattice and/or under an appropriate hydrostatic pressure may be good candidates for exploring the FFLO state.
In section II, the effects of magnetic vortices and nonmagnetic impurities on the low energy quasiparticle excitations and the spin-lattice relaxation rate are examined in the iron-based superconductors for the s±-, s-and d-wave pairing symmetries, respec-tively. The main effect of the vortices is to enhance the quasiparticle excitations and the spin-lattice relaxation rate for all symmetries, and leads to a T3dependence of the re-laxation rate followed by a nearly T-linearity at lower temperatures. This enhancement can only be seen for the s±-and d-wave symmetries in the presence of nonmagnetic impurities. These results suggest that the s±-wave and d-wave pairing states behave similarly in response to the magnetic field and nonmagnetic impurities, therefore it may be impossible to distinguish them on the basis of the measurements of spin-lattice relaxation rates when a magnetic field and/or impurity scatterings are present.
In section Ⅲ, we investigate the band renormalization, FS reconstruction and the symmetry of the superconducting gap in KyFe2-xSe2iron-based superconductors using a five-orbital model. We have found that the most favorable superconducting pairing symmetry mediated by the spin fluctuations is the dx2-y2-wave. By using the t-J1-J2-J3model, we have studied the distribution of the magnetic order in this system in the presence of the Fe vacancies. We have also analyzed the magnetic phase diagram and find a blocked checkerboard antiferromagnetic order in agreement with the experimental measurements.
引文
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