Home >> News >> News

ICQM Faculty member Xiong-Jun Liu's group published a paper in Phys. Rev. Lett. addressing chiral Majorana modes protected by 2nd Chern numbers
《Physical Review Letters》报道量子材料科学中心刘雄军组有关第二陈数保护的手征Majorana费米子态

In a recent paper published Phys. Rev. Lett. (PRL 118,207002 (2017)), Dr. Cheung Chan and Prof. Xiong-Jun Liu proposed to study the emergent chiral Majorana modes protected by the 2nd Chern number in a 3D superconducting Weyl semimetal, and showed that such chiral Majorana modes obey a new type of 3D non-Abelian loop-braiding statistics.

The search for topological superconductors and non-Abelian Majorana modes ranks among the most fascinating topics in condensed matter physics. There now exist several fundamental superconducting phases which host symmetry protected or chiral Majorana modes, of which the chiral modes are protected by Chern numbers in even dimensions. In the present published paper, Dr. Chan and Prof. Liu proposed to observe novel chiral Majorana modes by realizing a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, i.e., the pair density wave (PDW) phase in a Weyl semimetal which breaks time-reversal symmetry. Without symmetry protection, the 3D gapped PDW phase is topologically trivial. However, a vortex line generated in such a phase can host chiral Majorana modes, which are shown to be protected by an emergent second Chern number of a synthetic 4D space generalized  from the PDW phase. More interestingly, Chan and Liu further show that these chiral modes in the vortex rings obey 3D non-Abelian loop-braiding statistics, which can be applied to topological quantum computation. These results may show insight into the study of new non-Abelian braiding statistics and topological phases in high dimension.

The work is supported by MOST, NSFC, and by Thousand Youth Talent Program of China.

 

Fig. 1:(a,b) Chiral gapless Majorana modes existing in the FFLO phase of a 3D superconducting Weyl semimetal, moving along the vortex lines and being protected by emergent 2nd Chern numbers; (c) In the BCS phase, no chiral Majorana modes, instead, the Majorana zero flat bands are obtained.

 

Fig. 2:The chiral Majorana modes in vortex rings obey 3D non-Abelian loop-braiding statistics.  (a) sketch for a single braiding; (b) the sketch for a full braiding.

近期,量子材料中心刘雄军研究员和该组成员陈章博士在Phys. Rev. Lett.发表论文(PRL 118,207002 (2017)),指出三维外尔半金属中在出现FFLO类型的超导配对时,可在其涡旋线中出现由第二陈数保护的手征无能隙马约拉纳(Majorana)激发,并证明该类手征Majorana激发在涡旋环(vortex ring)结构下,满足3-loop型的3D非阿贝尔统计特性。

寻找新型马约拉纳费米准粒子是近年凝聚态物理中的重要研究课题。马约拉纳准粒子的特征与所在超导体系的维度有着重要的关系。其中,由陈数(Chern number)保护的具有手征特性的马约拉纳准粒子通常存在于偶数维超导中,原因陈数是在偶数维空间中所定义。然而,在本工作中,陈章和刘雄军研究三维外尔半金属发现,当系统处于FFLO类型的超导配对时,在超导的涡旋线激发中出现手征无能隙马约拉纳态,且进一步表明,该手征特性的马约拉纳模不能由在二维空间定义的第一陈数保护。为此作者在原本的三维真实空间上,以超导相位作为参数空间,引入人工维度,进而研究由真实空间加人工维度形成的人造四维空间拓扑特性。他们计算发现在该四维空间中,系统的第二陈数非零,且提供了对前述涡旋线中手征马约拉纳态的拓扑保护。这个结论存在一系列非平凡推论,其中最有趣的是当考虑涡旋环结构时,该手征马约拉纳态可满足3-loop型的3D非阿贝尔统计。这对于研究高维空间的非阿贝尔统计性质以及新型拓扑物态提供了实际物理平台。

该工作由陈章博士后为第一作者,刘雄军研究员为通讯作者。文章得到国家自然科学基金,科技部重点专项,和国家青年千人基金的支持。

 

Fig. 1:(a,b) Chiral gapless Majorana modes existing in the FFLO phase of a 3D superconducting Weyl semimetal, moving along the vortex lines and being protected by emergent 2nd Chern numbers; (c) In the BCS phase, no chiral Majorana modes, instead, the Majorana zero flat bands are obtained.

 

Fig. 2:The chiral Majorana modes in vortex rings obey 3D non-Abelian loop-braiding statistics.  (a) sketch for a single braiding; (b) the sketch for a full braiding.