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Tunneling spectroscopy and Majorana modes emergent from topological gapless phases in high-T_c cuprate superconductors

机译：高T_c铜酸盐超导体中拓扑无隙相产生的隧道光谱和Majorana模式

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摘要

We explore possible signatures for observing Majorana fermions in the tunneling spectroscopy of high-T_c superconductors. It is shown that due to the Rashba spin-orbit interaction (α_R) generally introduced by contact electrode, in addition to the Heisenberg spin exchange interaction, the Dzyaloshinskii-Moriya and spin dipole-dipole interactions are induced. As a result, p-wave superconductivity is induced with the gap-function d vector being not aligned with the internal magnetic field of the spin-orbit interaction. For typical strength of the Rashba interaction, the induced p wave is weak. Hence, the resulting superconductor is still gapless and is not a topological superconductor. However, we find that the ground state undergoes a phase transition to a topological gapless phase with each nodal point originated from pure d wave being split into two stable nodal points characterized by the symmetry class DIII. Due to the splitting nodal structure, zero-energy Majorana modes always exist for any interfaces that are not exactly in (100) or (010) directions. Hence, for general interfaces, existence of Majorana modes is a robust feature. In addition, due to the nonalignedd vector, for (110) interfaces in which d wave is subdominant to p wave, there exist sizable dispersive Majorana edge states. Our results indicate that due to the presence of these Majorana modes, a small plateau in tunneling spectrum near zero-bias peak would be induced. Furthermore, zero-energy Majorana modes result in 4π periodicity in typical SIS' junctions with difference in orientations of S and S' being within 21°-39° for α_R = 0.05-0.3 eV. As a result, it is easy for a π ring in tricrystal experiments to hold Majorana fermions and exhibit periods of two flux quanta in external magnetic field. These phenomena may have been already observed in experiments and their connections to experimental results are discussed.
机译：我们探索在高T_c超导体的隧道光谱中观察马约拉纳费米子的可能特征。结果表明，由于通常由接触电极引入的Rashba自旋轨道相互作用（α_R），除了海森堡自旋交换相互作用之外，还引起了Dzyaloshinskii-Moriya和自旋偶极-偶极相互作用。结果，在间隙函数d矢量与自旋轨道相互作用的内部磁场不对齐的情况下，感应出了p波超导。对于Rashba相互作用的典型强度，所感应的p波是微弱的。因此，所得的超导体仍然是无间隙的，并且不是拓扑超导体。然而，我们发现基态经历了到拓扑无间隙相的相变，每个结点都源自纯d波，并被分成两个对称的DIII型稳定结点。由于节点结构分裂，对于不完全在（100）或（010）方向上的任何接口，始终存在零能量Majorana模式。因此，对于通用接口，Majorana模式的存在是一个强大的功能。另外，由于矢量的不对齐，对于（110）d波次于p波的界面，存在相当大的弥散Majorana边缘态。我们的结果表明，由于这些Majorana模式的存在，隧道谱中接近零偏峰的区域将产生一个小的平台。此外，零能量Majorana模式在典型的SIS'结中产生4π周期性，并且对于α_R= 0.05-0.3 eV，S和S'的方向差异在21°-39°之内。结果，在三晶体实验中，π环很容易保留马约拉那费米子，并在外部磁场中表现出两个磁通量的周期。这些现象可能已经在实验中观察到，并讨论了它们与实验结果的关系。

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  • 来源
    《Physical review》 |2015年第13期|134501.1-134501.14|共14页
  • 作者

    Jun-Ting Kao; Shin-Ming Huang; Chung-Yu Mou; C. C. Tsuei;

  • 作者单位

    Department of Physics, National Tsing Hua University, Hsinchu 30043, Taiwan;

    Graphene Research Centre and Department of Physics, National University of Singapore, Singapore 117542;

    Department of Physics, National Tsing Hua University, Hsinchu 30043, Taiwan ,Institute of Physics, Academia Sinica, Nankang, Taiwan ,Physics Division, National Center for Theoretical Sciences, P.O. Box 2-131, Hsinchu, Taiwan;

    IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA;

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  • 关键词

    surface states, band structure, electron density of states; quantum wires;

    机译：表面态;能带结构;态电子密度;量子线;

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