arXiv 1012.00572010-12cond-mat.supr-concond-mat.mes-hall

自旋轨道耦合系统中拓扑非平凡超导性：体相和量子相变

Topologically non-trivial superconductivity in spin-orbit coupled systems: Bulk phases and quantum phase transitions

Sumanta Tewari, Tudor D. Stanescu, Jay D. Sau, S. Das Sarma

备注：: as published in the focus issue on Topological Quantum Computation, New J. Phys. 13 (2011)
发表信息：: New J. Phys. 13, 065004 (2011)
DOI：: 10.1088/1367-2630/13/6/065004

摘要：

拓扑非平凡的超导性已经被预测发生在具有相当大的自旋轨道耦合的超导体中，在外部塞曼分裂的存在下。已经提出了两个这样的系统：（a）s波超导体对势是在半导体上邻近感生的，以及（b）对势自然地产生于固有的s波配对相互作用。如现在所熟知的，以2D膜或线网络中的1D纳米线的形式的这种系统可以用于拓扑量子计算。当外部塞曼分裂$Γ$超过一个临界值$Γ_c$时，系统从规则超导相过渡到非阿贝尔拓扑超导相。在（a）和（b）两种情况下，本文都考虑对势$Δ$在普通相和拓扑超导相中都是严格s波，它们被一个位于$Γ_c = \sqrt{Δ^2 + μ^2}$的拓扑量子临界点分开，其中$μ(>> Δ)$是化学势。另一方面，由于存在$Γ_c >> Δ$，拓扑相（$Γ> Γ_c$）所需的塞曼分裂远远超过值（$Γ\sim Δ$），在没有自旋轨道耦合的情况下，高于该值，s波对势将消失（并且系统将变为非超导）。因此，我们导致的情况下，拓扑超导相似乎设置在一个参数制度，该系统实际上是非超导的自旋轨道耦合的情况下。在本文中，我们解决的问题是如何一个纯的s波对潜力可以生存一个强大的塞曼场产生的拓扑超导相。我们表明，自旋-轨道耦合是量子跃迁和拓扑非平凡超导相实现$Γ>> Δ$的鲁棒性的关键参数。

英文摘要：

Topologically non-trivial superconductivity has been predicted to occur in superconductors with a sizable spin-orbit coupling in the presence of an external Zeeman splitting. Two such systems have been proposed: (a) s-wave superconductor pair potential is proximity induced on a semiconductor, and (b) pair potential naturally arises from an intrinsic s-wave pairing interaction. As is now well known, such systems in the form of a 2D film or 1D nano-wires in a wire-network can be used for topological quantum computation. When the external Zeeman splitting $Γ$ crosses a critical value $Γ_c$, the system passes from a regular superconducting phase to a non-Abelian topological superconducting phase. In both cases (a) and (b) we consider in this paper the pair potential $Δ$ is strictly s-wave in both the ordinary and the topological superconducting phases, which are separated by a topological quantum critical point at $Γ_c = \sqrt{Δ^2 + μ^2}$, where $μ(>> Δ)$ is the chemical potential. On the other hand, since $Γ_c >> Δ$, the Zeeman splitting required for the topological phase ($Γ> Γ_c$) far exceeds the value ($Γ\sim Δ$) above which an s-wave pair potential is expected to vanish (and the system to become non-superconducting) in the absence of spin-orbit coupling. We are thus led to a situation that the topological superconducting phase appears to set in a parameter regime at which the system actually is non-superconducting in the absence of spin-orbit coupling. In this paper we address the question of how a pure s-wave pair potential can survive a strong Zeeman field to give rise to a topological superconducting phase. We show that the spin-orbit coupling is the crucial parameter for the quantum transition into and the robustness of the topologically non-trivial superconducting phase realized for $Γ>> Δ$.

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