Bogoliubov Fermi surfaces: General theory, magnetic order, and topology
Bogoliubov Fermi surfaces: General theory, magnetic order, and topology
复制标题
DOI：
10.1103/physrevb.98.224509
复制
发表时间：
2018-12-14
影响因子：
3.7
通讯作者：
Timm, C.
中科院分区：
文献类型：
--
作者：
Brydon, P. M. R.;Agterberg, D. F.;Timm, C.
我们提出了一个全面的理论Bogoliubov费米面的反演对称超导体，打破时间反演对称。这种带隙结构的要求是电子具有与自旋分离的内部自由度（例如，轨道或亚晶格指数），这允许库珀对的非平凡内部结构。在破坏时间反演对称性的配对状态下，库珀对在内部自由度上一般是极化的，类似于非幺正三重态超导体中的自旋极化配对。我们表明，这种极化可以量化的差距产品的时间反转奇数部分，即，对势与其厄米共轭的矩阵乘积。这个乘积对于Bogoliubov Fermi曲面的出现和它们的Z（2）不变量的拓扑保护是必不可少的。在研究了Bogoliubov费米表面在一个通用的双带模型的外观后，我们继续研究两个具体的情况：一个立方材料与j = 3/2的总角动量自由度和一个六角形材料与不同的轨道和自旋自由度。对于这些模型系统，我们表明，极化配对产生的低能量状态的磁化。我们还计算了与这些配对状态相关的表面光谱，并证明了Bogoliubov费米表面的特征在于额外的拓扑指数。最后，我们讨论了超导体的唯象理论的扩展，包括Bogoliubov费米面，并确定的库珀对的时间反演奇极化作为一个复合序参量，这是交织在一起的超导性。
We present a comprehensive theory for Bogoliubov Fermi surfaces in inversion-symmetric superconductors which break time-reversal symmetry. A requirement for such a gap structure is that the electrons posses internal degrees of freedom apart from the spin (e.g., orbital or sublattice indices), which permits a nontrivial internal structure of the Cooper pairs. In a pairing state that breaks time-reversal symmetry, the Cooper pairs are generically polarized in the internal degrees of freedom, in analogy to spin-polarized pairing in a nonunitary triplet superconductor. We show that this polarization can be quantified in terms of the time-reversal-odd part of the gap product, i.e., the matrix product of the pairing potential with its Hermitian conjugate. This product is essential for the appearance of Bogoliubov Fermi surfaces and their topological protection by a Z(2) invariant. After studying the appearance of Bogoliubov Fermi surfaces in a generic two-band model, we proceed to examine two specific cases: a cubic material with a j = 3/2 total-angular-momentum degree of freedom and a hexagonal material with distinct orbital and spin degrees of freedom. For these model systems, we show that the polarized pairing generates a magnetization of the low-energy states. We additionally calculate the surface spectra associated with these pairing states and demonstrate that the Bogoliubov Fermi surfaces are characterized by additional topological indices. Finally, we discuss the extension of phenomenological theories of superconductors to include Bogoliubov Fermi surfaces, and identify the time-reversal-odd polarization of the Cooper pairs as a composite order parameter, which is intertwined with superconductivity.