Non-Abelian topological order in noncentrosymmetric superconductors with broken time-reversal symmetry
Non-Abelian topological order in noncentrosymmetric superconductors with broken time-reversal symmetry
复制标题
DOI：
10.1103/physrevb.82.184525
复制
发表时间：
2010-11-16
影响因子：
3.7
通讯作者：
Das Sarma, S.
中科院分区：
文献类型：
--
作者：
Ghosh, Parag;Sau, Jay D.;Das Sarma, S.
我们考虑了二维非中心对称超导体，其中序参数是S波和p波的混合体，存在外感应塞曼分裂。给出了系统处于非阿贝尔相的条件。通过考虑涡旋Bogoliubov-de Gennes(BdG)方程的非简并零能Majorana解，通过构造一个拓扑不变量，证明了非阿贝尔相存在的条件与三重态对的振幅完全无关。从BdG方程的实空间解得到的非阿贝尔相的存在条件涉及到BdG哈密顿量在k=0时的Pfaffian，它对序参数的p波分量的大小完全不敏感。通过对这种情况使用适当的拓扑不变量，我们得到了同样的结论。这与时间反转不变拓扑相的类似条件形成鲜明对比，即P波分量的幅度必须大于序参数的S波片的幅度。作为副产品，我们建立了在k=0时BdG哈密顿量的Pfaffian与相应的Z拓扑不变量之间的内在联系。
We consider two-dimensional noncentrosymmetric superconductors, in which the order parameter is a mixture of s-wave and p-wave parts, in the presence of an externally induced Zeeman splitting. We derive the conditions under which the system is in a non-Abelian phase. By considering the nondegenerate zero-energy Majorana solutions of the Bogoliubov-de Gennes (BdG) equations for a vortex and by constructing a topological invariant, we show that the condition for the non-Abelian phase to exist is completely independent of the triplet pairing amplitude. The existence condition for the non-Abelian phase derived from the real-space solutions of the BdG equations involves the Pfaffian of the BdG Hamiltonian at k=0, which is completely insensitive to the magnitude of the p-wave component of the order parameter. We arrive at the same conclusion by using the appropriate topological invariant for this case. This is in striking contrast to the analogous condition for the time-reversal invariant topological phases, in which the amplitude of the p-wave component must be larger than the amplitude of the s-wave piece of the order parameter. As a by-product, we establish the intrinsic connection between the Pfaffian of the BdG Hamiltonian at k=0 (which arises at the BdG approach) and the relevant Z topological invariant.