Majorana vortex-bound states in three-dimensional nodal noncentrosymmetric superconductors

Chang, Po-Yao; Matsuura, Shunji; Schnyder, Andreas P.; Ryu, Shinsei

doi:10.1103/physrevb.90.174504

Cited by 14 publications

(13 citation statements)

References 65 publications

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“…The vortex can be considered as a small hole in the superconductor; since |Ch| = 1 in the spinless chiral p-wave superconductor, the boundary of the small hole supports a gapless boundary state, which eventually becomes a zero-energy state (called "zero mode") when localized in the vortex core [12,51]. Vortices in a variety of topological superconductors may support zero modes in a similar manner [66][67][68][69].…”

Section: Topological Boundary and Defect Statesmentioning

confidence: 99%

Topological superconductors: a review

Sato¹,

Ando²

2017

Rep. Prog. Phys.

1,460

1,103

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This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors. CONTENTS

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Section: Topological Boundary and Defect Statesmentioning

confidence: 99%

Topological superconductors: a review

Sato¹,

Ando²

2017

Rep. Prog. Phys.

1,460

1,103

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“…We observe that the unstable nodal superconductor (16) can be connected to a fully gapped topological superconductor without removing the zero-energy edge states. That is, the edge states of Hamiltonian (16) are inherited from the fully gapped topological phase [72].…”

Section: As Indicated Inmentioning

confidence: 99%

“…That is, the unstable nodal superconductor (63) is connected to the fully gapped reflection-symmetric topological superconductor (64) and inherits topological edge states from the fully gapped phase [72].…”

Section: Unstable Reflection-symmetric Nodal Superconductors (Class Dmentioning

confidence: 99%

Classification of reflection-symmetry-protected topological semimetals and nodal superconductors

2014

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While the topological classification of insulators, semimetals, and superconductors in terms of nonspatial symmetries is well understood, less is known about topological states protected by crystalline symmetries, such as mirror reflections and rotations. In this work, we systematically classify topological semimetals and nodal superconductors that are protected, not only by nonspatial (i.e., global) symmetries, but also by a crystal reflection symmetry. We find that the classification crucially depends on (i) the codimension of the Fermi surface (nodal line or point) of the semimetal (superconductor), (ii) whether the mirror symmetry commutes or anticommutes with the nonspatial symmetries, and (iii) how the Fermi surfaces (nodal lines or points) transform under the mirror reflection and nonspatial symmetries. The classification is derived by examining all possible symmetry-allowed mass terms that can be added to the Bloch or Bogoliubov-de Gennes Hamiltonian in a given symmetry class and by explicitly deriving topological invariants. We discuss several examples of reflection-symmetry-protected topological semimetals and nodal superconductors, including topological crystalline semimetals with mirror Z 2 numbers and topological crystalline nodal superconductors with mirror winding numbers.

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“…Note that the vortex (antivortex) is defined by a positive (negative) winding number C arg[∆(r)] ds about the vortex (antivortex) core, where C is a small circle centered at the core. The function that parametrizes the phase of the vortex/antivortex pair is given by 41 φ(x, y) = tan −1 2ayC(y)…”

Section: A Implementation Of Vortex/antivortex Pairmentioning

confidence: 99%

Structure of vortex-bound states in spin-singlet chiral superconductors

Lee

Schnyder

2016

Phys. Rev. B

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We investigate the structure of vortex-bound states in spin-singlet chiral superconductors with (d x 2 −y 2 ± idxy)-wave and (dxz ± idyz)-wave pairing symmetries. It is found that vortices in the (dxz ± idyz)-wave state bind zero-energy states which are dispersionless along the vortex line, forming a doubly degenerate Majorana flat band. Vortex-bound states of (d x 2 −y 2 ± idxy)-wave superconductors, on the other hand, exist only at finite energy. Using exact diagonalization and analytical solutions of tight-binding Bogoliubov-de Gennes Hamiltonians, we compute the energy spectrum of the vortex-bound states and the local density of states around the vortex and antivortex cores. We find that the tunneling conductance peak of the vortex is considerably broader than that of the antivortex. This difference can be used as a direct signature of the chiral order parameter symmetry.

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Majorana vortex-bound states in three-dimensional nodal noncentrosymmetric superconductors

Cited by 14 publications

References 65 publications

Topological superconductors: a review

Topological superconductors: a review

Classification of reflection-symmetry-protected topological semimetals and nodal superconductors

Structure of vortex-bound states in spin-singlet chiral superconductors

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