Impurity-generated non-Abelions

G. Simion; A. Kazakov; L. P. Rokhinson; T. Wojtowicz; Y. B. Lyanda-Geller

摘要

Two classes of topological superconductors and Majorana modes in condensed matter systems are known to date: one in which disorder induced by impurities strongly suppresses topological superconducting gap and is detrimental to Majorana modes, and another where Majorana fermions are protected by a disorder-robust topological superconductor gap. Observation and control of Majorana fermions and other non-Abelions often requires a symmetry of an underlying system leading to a gap in the single-particle or quasiparticle spectra. In semiconductor structures, impurities that provide charge carriers introduce states into the gap and enable conductance and proximity-induced superconductivity via the in-gap states. Thus a third class of topological superconductivity and Majorana modes emerges, in which topological superconductivity and Majorana fermions appear exclusively when impurities generate in-gap states. We show that impurity-enabled topological superconductivity is realized in a quantum Hail ferromagnet, when a helical domain wall is coupled to an s-wave superconductor. As an example of emergence of topological superconductivity in quantum Hall ferromagnets, we consider the integer quantum Hall effect in Mn-doped CdTe quantum wells. Recent experiments on transport through the quantum Hall ferromagnet domain wall in this system indicated a vital role of impurities in the conductance, but left unresolved the question whether impurities preclude generation of Majorana fermions and other non-Abelions in such systems in general. Here, solving a general quantum-mechanical problem of impurity bound states in a system of spin-orbit coupled Landau levels, we demonstrate that impurity-induced Majorana modes emerge at boundaries between topological and conventional superconducting states generated in a domain wall due to proximity to an s superconductor. We consider both short-range disorder and a smooth random potential. The phase diagram of the system is defined by characteristic disorder, gate voltage induced angular momentum splitting of impurity levels, and by a proximity superconducting gap. The phase diagram exhibits two ranges of gate voltage with conventional superconducting order separated by a gate voltage range with topological superconductivity. We show that electrostatic control of domain walls in an integer quantum Hall ferromagnet allows manipulation of Majorana fermions. Ferromagnetic transitions in the fractional quantum Hall regime may lead to the formation and electrostatic control of higher order non-Abelian excitations.

机译：迄今已知凝聚态系统中的两类拓扑超导体和Majorana模态：一种由杂质引起的无序强烈抑制拓扑超导能隙，并且对Majorana模态有害；另一类其中Majorana费米子受到无序鲁棒拓扑超导体的保护。间隙。观察和控制马约拉纳费米子和其他非阿贝里斯通常需要对称的下层系统，导致单粒子或准粒子光谱出现缺口。在半导体结构中，提供电荷载流子的杂质将状态引入间隙中，并通过间隙内状态实现电导和接近感应超导性。因此，出现了第三类拓扑超导和马约拉那模式，其中当杂质产生间隙状态时，拓扑超导和马约拉那费米子只出现。我们显示，当螺旋畴壁耦合到s波超导体时，在量子雹铁磁体中实现了杂质使能的拓扑超导。作为量子霍尔铁磁体中拓扑超导出现的一个例子，我们考虑了Mn掺杂CdTe量子阱中的整数量子霍尔效应。最近在该系统中通过量子霍尔铁磁体畴壁传输的实验表明，杂质在电导中起着至关重要的作用，但仍未解决以下问题：杂质在总体上是否会排除马约拉纳费米子和其他非阿贝尔离子的产生。在这里，解决了自旋轨道耦合Landau能级系统中杂质结合态的一般量子力学问题，我们证明了杂质诱导的Majorana模出现在畴壁产生的拓扑和常规超导态之间的边界，这是由于与超导体。我们同时考虑了短程障碍和平稳的随机潜力。系统的相图由特征无序，栅极电压引起的杂质能级角动量分裂以及邻近超导间隙定义。该相图显示了具有常规超导阶数的两个栅极电压范围，这些范围被具有拓扑超导性的栅极电压范围所分隔。我们表明，在整数量子霍尔铁磁体中对畴壁的静电控制允许对马里亚纳费米子的操纵。分数量子霍尔机制中的铁磁跃迁可能导致高阶非阿贝尔激发的形成和静电控制。

Impurity-generated non-Abelions

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