Magnetic Response of Majorana Kramers Pairs Protected by \(\mathbb{Z}_{2}\) Invariants

Yamazaki, Yoji; Kobayashi, Shingo; Yamakage, Ai

doi:10.7566/jpsj.89.043703

Cited by 12 publications

(6 citation statements)

References 74 publications

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“…Thus, the magnetic response of MKPs gives a way to identify unconventional Cooper pairs in TSCs. More recently, we extended the above discussion to the case of MKPs ensured by crystalline symmetry-protected Z 2 invariant, and revealed that TSCs with nonsymmorphic symmetry naturally host two MKPs, leading to an electric quadrupole response 65,66 .…”

Section: Introductionmentioning

confidence: 76%

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Majorana multipole response: General theory and application to wallpaper groups

Kobayashi,

Yamazaki,

Yamakage

et al. 2020

Preprint

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Emergent Majorana fermions on surfaces of time-reversal invariant topological superconductors host electromagnetic structures and realize unique electromagnetic responses. In this paper, we develop a general theory of electric and magnetic responses of the surface Majorana fermions on time-reversal invariant superconductors, on the basis of topological classification and the group theory. In particular, we provide a classification of possible electromagnetic responses of the emergent Majorana fermions arising from the interplay between topology and crystalline symmetry. It is found that the emergent Majorana fermions host magnetic structures with dipole or octupole order, and the magnetic response of a single Majorana Kramers pair directly links to Cooper pair symmetry: the magnetic structure and the Cooper pairs have a common irreducible representation under crystalline symmetry. This result provides a new perspective for the identification of unconventional Cooper pairings in topological superconductors through surface-spin-sensitive measurements. We also identify a set of crystalline symmetries without magnetic dipole response, which leads to a magnetic octupole response as the leading contribution. Such a magnetic octupole response provides a unique indication of exotic topological superconductors like topological superconductors associated with J = 3/2 electrons or nonsymmorphic symmetry. We also clarify that multiple Kramers pairs give an electric response.

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Section: Introductionmentioning

confidence: 76%

“…In order that Ĥm is invariant under G k 0 , g + (B) (g − (B)) and ÔMF+ ( ÔMF− ) should be the same irrep under the transformation in Eqs. ( 64) and (65).…”

Section: E Electric and Magnetic Couplings Of Mkpsmentioning

confidence: 99%

Majorana multipole response: General theory and application to wallpaper groups

Kobayashi,

Yamazaki,

Yamakage

et al. 2020

Preprint

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“…An interesting extension of our study is for topological superconductors, on Majorana fermions The surface Majorana fermions timereversal-invariant topological have only Ising of freedom for called Majorana Ising spins. Furthermore, an octupole [29] and an (electric) quadrupole [30] of Majorana fermions can be coupled to a magnetic that the magnetic-texture-induced Hall effect is used to detect Majorana fermions and their magnetic degrees of freedom; this will be discussed in a future work.…”

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confidence: 99%

Theory of Magnetic-Texture-Induced Anomalous Hall Effect on the Surface of Topological Insulators

Yamaguchi,

Yamakage

2021

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The anomalous Hall effect is caused by magnetic textures such as skyrmions. We derive an analytical formula of the Hall conductivity on the surface of a topological insulator up to third order in magnetization, M(x), based on a perturbative approach. We identify the magnetic textures that contribute to the Hall conductivity up to third order in magnetization and second order in spatial differentiation. We treat magnetization as a perturbation to calculate the Hall conductivity for each magnetic texture based on the linear response theory. Furthermore, we estimate the skyrmion-induced Hall conductivity and confirm that it depends on the shape of skyrmions, such as Bloch-type or Néel-type skyrmions. The results of this study can be applied not only to conventional skyrmion systems but also to more general magnetic structures.

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“…It has previously been revealed that double MKPs protected by crystalline symmetry can respond to an electric perturba-tion. 44) The electric responses of MKPs have also been classified for each superconducting pair potential when the symmetry of the surface is or 4 wallpaper group (WG). 43) Thus, although several properties of the electrical response of double MKPs have been clarified discursively, this study comprehensively clarifies new aspects of the electrical response from a different perspective.…”

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confidence: 99%

“…These phenomena have been systematically classified. 27-30, 32, 45) According to these classifications, double MKPs can only exist in magnetic chiral-and/or glide-planesymmetric systems, 30,42,44,46) as described below.…”

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confidence: 99%

Electric Multipoles of Double Majorana Kramers Pairs

Yamazaki,

Kobayashi,

Yamakage

2021

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A single Majorana Kramers pair hosts only one component of the magnetic multipole. This can be used to determine the bulk Cooper-pair symmetry through surface-sensitive spectroscopic measurements, either by applying a magnetic field or by using a ferromagnet/superconductor junction. This paper proposes that the electric response, which is free from the Meissner effect, can be used an alternative method to measure the bulk Cooper-pair symmetry in time-reversal-invariant superconductors with double Majorana Kramers pairs. The relationships among electric multipoles, strain tensors and superconducting symmetries under a given wallpaper group on the surfaces of topological crystalline superconductors are shown. This study also reveals that only a specific irreducible representation of a uniform strain yields a gap in the double Majorana Kramers pairs for the topological-crystalline-superconductor candidate Sr 3 SnO. This highlights the viability of electric detection regarding Cooper-pair symmetry.

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Magnetic Response of Majorana Kramers Pairs Protected by \(\mathbb{Z}_{2}\) Invariants

Cited by 12 publications

References 74 publications

Majorana multipole response: General theory and application to wallpaper groups

Majorana multipole response: General theory and application to wallpaper groups

Theory of Magnetic-Texture-Induced Anomalous Hall Effect on the Surface of Topological Insulators

Electric Multipoles of Double Majorana Kramers Pairs

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