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Stability of Majorana bound states in the presence of spin-flip scattering
Physica E: Low-dimensional Systems and Nanostructures ( IF 3.3 ) Pub Date : 2020-10-03 , DOI: 10.1016/j.physe.2020.114389
Subhajit Pal , Colin Benjamin

A popular evidence of the existence of Majorana bound states (MBS) is a quantized zero-bias conductance peak (ZBCP) which is robust to scattering by impurities, a consequence of its topological protection. In this work we examine the stability of this MBS induced ZBCP in a metal-superconductor junction in the vicinity of a spin flipper. We analytically calculate the differential charge conductance for metal-spin flipper-superconductor junctions with two distinct types of superconductors: (a) spin less p-wave superconductor and (b) spin-orbit-coupled s-wave superconducting wire in presence of a Zeeman field (SOCSW). We see that the quantized ZBCP remains stable in presence of spin flip scattering for metal-p-wave superconductor junction, while it loses its stability when the p-wave superconductor is replaced by a SOCSW. Further, the scattering matrix of the normal metal-p-wave superconductor junction satisfies BDI symmetry class regardless of the presence or absence of spin flip scattering. In the BDI symmetry class both Hamiltonian as well as scattering matrix satisfies particle-hole, time reversal and chiral symmetries. However, in case of normal metal-SOCSW junction the Hamiltonian as well as scattering matrix belongs to symmetry class D in absence of spin flip scattering. In the symmetry class D both Hamiltonian and the scattering matrix satisfy particle-hole symmetry relation, but do not satisfy time reversal and chiral symmetry relations. In presence of spin flip scattering the scattering matrix for SOCSW belongs to symmetry class A for which the scattering matrix does not satisfy either particle-hole or time reversal or chiral symmetry relations. The reason for ZBCP at a metal-p wave superconductor junction is perfect Andreev reflection regardless of spin flip scattering, while for a metal-SOCSW junction it is the exact cancellation between normal and Andreev reflection probabilities at zero bias and not perfect Andreev reflection, in absence of spin flip scattering. In presence of spin flip scattering, on the other hand, there is no exact cancellation at zero bias which leads to absence of quantized ZBCP for a metal-SOCSW junction.



中文翻译:

自旋翻转散射下马约拉纳键态的稳定性

马约拉纳邦状态(MBS)的存在的流行证据是量化的零偏电导峰(ZBCP),由于其拓扑保护,该峰对杂质的散射具有鲁棒性。在这项工作中,我们研究了自旋鳍状板附近的MBS诱导的ZBCP在金属-超导体结中的稳定性。我们分析计算具有两种不同类型的超导体的金属自旋鳍状体-超导体结的差分电荷电导:(a)减少自旋p波超导体和(b)自旋轨道耦合的s波超导线,并存在塞曼场(SOCSW)。我们看到,量化的ZBCP在存在自旋翻转散射的情况下对于金属p波超导体结保持稳定,而当p波超导体被SOCSW取代时它失去了稳定性。此外,无论是否存在自旋翻转散射,普通金属-p-波超导体结的散射矩阵都满足BDI对称性类别。在BDI对称性类别中,哈密顿量和散射矩阵都满足粒子-孔,时间反转和手性对称性。但是,在正常金属-SOCSW结的情况下,在没有自旋翻转散射的情况下,哈密顿量和散射矩阵都属于对称性D类。在对称性D类中,哈密顿量和散射矩阵均满足粒子-孔对称关系,但不满足时间反转和手性对称关系。在存在自旋翻转散射的情况下,SOCSW的散射矩阵属于对称性A类,其散射矩阵不满足粒子-孔或时间反转或手性对称关系。不管自旋翻转散射如何,金属p波超导体结处的ZBCP都是完美的Andreev反射,而对于金属-SOCSW结,这是零偏置下法向和Andreev反射概率之间的精确抵消,而在Andreev反射中则不是完美的。没有自旋翻转散射。另一方面,在存在自旋翻转散射的情况下,

更新日期:2020-10-06
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