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ICQM Xiong-Jun Liu’s group published a paper in Phys. Rev. Lett. addressing generic theory for non-Abelian Majorana zero modes
《Physical Review Letters》报道量子材料中心刘雄军组有关非阿贝尔Majorana零模的一般化理论工作

In a recent paper published Phys. Rev. Lett. (PRL 119, 047001 (2017)), Prof. Xiong-Jun Liu and his team developed a generic theory for non-Abelian Majorana zero modes in 2D superconductors and superfluids. They showed that the Majorana zero modes can be generically obtained in a superconductor/superfluid with topologically trivial or nontrivial bulk, and further proposed a minimal experimental scheme for the realization of Majorana zero modes.

It is well known that non-Abelian Majorana zero modes are located at vortex cores in a chiral topological superconductor, which can be realized in a 2D spin-orbit coupled system with a single Fermi surface and by proximity coupling to an s-wave superconductor. In particular, the experimental proposals for realizing Majorana zero modes have been largely built on the realization of topological superconductors. However, Majorana zero modes in superconductors are topological defect modes, which correspond to nonlocal extrinsic deformations in the Hamiltonian of the topological system. For example, Majorana zero modes in the chiral px+ipy superconductor are located at vortices that exhibit nonlocal phase windings of the superconductor order (a global deformation in the original uniform Hamiltonian). This feature tells us that the Majorana zero modes at vortices are not intrinsic topological excitations, but extrinsic modes of a superconductor. In this regard, one may conjecture that the existence of MZMs does not uniquely correspond to the bulk topology of a superconductor, and there might be much broader range of experimental systems that can host such exotic modes, besides those based on topologically nontrivial superconductors.

Motivated by the above consideration, Dr. Cheung Chan, PhD student Lin Zhang etal in Prof. Xiong-Jun Liu’s group show that the existence of non-Abelian Majorana zero modes is unrelated to the bulk topology of a 2D superconductor, and propose that such exotic modes can result in a much broader range of superconductors, being topological or trivial. For a generic 2D system with multiple Fermi surfaces that is gapped out by superconducting pairings, they show that at least a single Majorana zero mode survives if there are only an odd number of Fermi surfaces of which the corresponding superconducting orders have vortices; such a Majorana zero mode is protected by an emergent Chern-Simons invariant, irrespective of the bulk topology of the superconductor. This result enriches new experimental schemes for realizing non-Abelian Majorana zero modes. In particular, they propose a minimal scheme to realize the Majorana zero modes in a 2D superconducting Dirac semimetal with trivial bulk topology, which can be well achieved based on recent cold-atom experiment performed by Xiong-Jun Liu’s group collaborating with a USTC team (Science 354, 83-88 (2016)).

The work is supported by MOST, NNSFC, and Thousand-Youth-Talent program.

 

Figure 1: Non-Abelian Majorana zero modes obtained in 2D superconductor/suerpfluid with a trivial bulk.

  近期,量子材料中心刘雄军研究员在Phys. Rev. Lett.发表论文(PRL 119, 047001 (2017)),提出二维超导体/超流系中马约拉纳(Majorana)零模出现的一般化理论。该理论指出,非阿贝尔Majorana零能模的出现和其超导/超流载体本身的拓扑特性无关,即无论在拓扑平凡或非平凡的二维超导或超流中,均可以获得满足非阿贝尔统计的马约拉纳零能模,并由此提出实现马约拉纳零能模的最小化物理实验模型。该工作是该研究组近期在有关非阿贝尔马约拉纳态的系列工作之一,与之前该组发表在PRL上的另一篇论文(PRL 118, 207002 (2017))形成对不同维度超导及超流体系中实现非阿贝尔马约拉纳模的系统研究。

  寻找满足非阿贝尔交换统计的马约拉纳准粒子是当前凝聚态物理中的重要研究课题。一般认为,马约拉纳零能模可以边缘态或者涡旋模式的形式存在于不同维度的拓扑超导中。获得拓扑超导是目前普遍认为实现马约拉纳零能模的基本手段。然而,无论存在于超导边缘,或是超导涡旋激发中,马约拉纳零模并非其超导载体的内秉激发(intrinsic excitation),而属于外在激发(extrinsic excitation)。这是因为,比如涡旋,属于拓扑缺陷,产生涡旋需要对原始超导系统做非局域(nonlocal)的改变(涡旋本身具有非零拓扑缠绕数)。因此,产生涡旋,实际已经改变原来的超导本身,其承载的准粒子态并非对应原始超导本身的体拓扑特性。因此,马约拉纳零能模的出现可完全与超导本身的拓扑特性无关。为此刘雄军与该组成员陈章,张林等人对马约拉纳零能模出现的一般化理论进行研究,指出马约拉纳零能模的形成与其载体拓扑无关,而是由更高维虚拟空间拓扑量刻画。对于二维体系而言,他们证明马约拉纳零能模是由定义在三维空间的陈-西蒙斯量决定。该理论表明,马约拉纳零能模实际可存在于更广泛的拓扑平凡或非平凡超导/超流体系中。为此,该研究组提出了实现马约拉纳零能模的最小化物理实验模型。特别指出,该模型可在冷原子中基于刘雄军研究组和中国科大合作实现的人工二维Dirac型自旋轨道耦合而实现(该工作发表于去年的国际权威期刊《科学》上:Science 354, 83-88 (2016)。为超冷原子近两年的一项重要进展)。

  该工作可进一步推广至一般情形,包括任意不同维度的拓扑平凡或非平凡体系,以及存在对称保护时的各种不同情形。这些推广将导致更丰富的新的新奇物态,以及高维空间中的非阿贝尔统计,大大拓宽人们对该类新奇物态的理解。相关工作正在进一步推进中。该工作由该组博士生张林和博士后陈章为共同第一作者,其他作者包括该组博士生潘挺峰,何映萍,以及本科生王彦琦,均有不同程度贡献。刘雄军为通讯作者。工作在科技部重点专项,自然科学基金,以及青年千人基金支持下完成。

 

图1:二维平凡超导的涡旋中心形成马约拉纳零能模。