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

Lee, Darrick; Schnyder, Andreas P.

doi:10.1103/physrevb.93.064522

Cited by 8 publications

(12 citation statements)

References 54 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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“…The only difference is that the d xz + id yz states has odd chirality N = 1, and thus the spectrum contains in addition the branch with n = 0, which forms the flat band with zero energy for |p z | < p 0 , where p 0 marks the position of the Weyl point. 9 This flat band arises from the Weyl points in bulk, as it happens in vortices in chiral Weyl superfluid 3 He-A in Fig. 1 (right)).…”

mentioning

confidence: 89%

“…Examples are provided by vortices 12 in the recently discovered 13 zeroes, 14 such as the chiral (N = 1) spin-singlet superconductor with (d xz + id yz ) pairing. 9 We start with the polar phase, whose order parameter matrix is∆…”

Section: Pacs Numbersmentioning

confidence: 99%

“…Such pairing has been suggested in the heavy-fermion compound URu 2 Si 2 . 10,11 The n = 0 level with the flat band does not appear in the core of superconductors with (d x 2 −y 2 + id xy )-wave pairing, 9 where the gap ∆(p) ∝ (p x + ip y ) 2 has N = 2, and the spectrum contains the Weyl points with double topological charge and quadratic dispersion. 3 Here we consider vortices, in which the minigap ω 0 (p z ) vanishes at p z = 0.…”

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confidence: 99%

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Condensation of fermion zero modes in the vortex

Volovik

2016

Jetp Lett.

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The energy levels of the fermions bound to the vortex are considered for vortices in the superfluid/superconducting systems which contain the symmetry protected plane of zeroes in the gap function in bulk. The Caroli-de Gennes-Matricon branches with different angular momentum quantum number n approach zero energy level at pz → 0. Such condensation of the energy levels is the consequence of the bulk-vortex correspondence in topological superfluids/superconductors. In a given case this is the connection between the Dirac line of zeroes in the bulk spectrum and the level condensation in the vortex core. The density of states of the bound fermions diverges at zero energy giving rise to the √ Ω dependence of DoS in the polar phase of superfluid 3 He rotating with the angular velocity Ω and to the √ B dependence of DoS for superconductors in the (dxz + idyz)-wave pairing state. PACS numbers:The spectrum of the low-energy bound states in the core of the symmetric vortex with winding number m = ±1 in the isotropic model of s-wave superconductor was obtained in a microscopic (BCS) theory by Caroli, de Gennes and Matricon, 1 see Fig. 1 (left):Here p z is the momentum of the bound states along the vortex line, and n is related to the angular momentum quantum number L z . This spectrum is two-fold degenerate due to spin degrees of freedom. The level spacing -the so called minigap -is small compared to the energy gap of the quasiparticles outside the core, ω 0 ∼ ∆ 2 /E F ∆. For the chiral superfluid/superconductor with an odd winding number of the phase of the gap function in momentum space (i.e. ∆(p) ∝ (p x + ip y ) N with odd N ), the spectrum of fermions in the symmetric vortex is modified, 2,3 see Fig. 1 (right) for the most symmetric vortex in the Weyl superfluid 3 He-A:The spectrum contains the zero energy states at n = 0. In the two-dimensional case the n = 0 levels represent two Majorana modes. 4,5 The 2D half-quantum vortex, which is the vortex in one spin component, contains single Majorana mode. In the 3D case the Eq.(2) at n = 0 describes the flat band in the spectrum of the bound states:6 all the states in the interval −p 0 < p z < p 0 have zero energy, where p 0ẑ and −p 0ẑ mark the positions of two Weyl points in the bulk material.7 The connection between the positions of the Weyl points in bulk, and the boundary of the flat band in the vortex core is the consequence of the bulk-vortex correspondence in topological materials. For numerical simulation of the flat band in the core of the 3 He-A vortex see Ref.8 . The n = 0 level with the flat band appears also in spin-singlet superconductors with (d xz + id yz )-wave pairing. 9This is because the gap function ∆(p) ∝ p z (p x + ip y ) has an odd chirality number N = 1 and the Weyl points in bulk. Such pairing has been suggested in the heavy-fermion compound URu 2 Si 2 .10,11 The n = 0 level with the flat band does not appear in the core of superconductors with (d x 2 −y 2 + id xy )-wave pairing, 9 where the gap ∆(p) ∝ (p x + ip y ) 2 has N = 2, and the spectrum co...

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“…Note that the definition of the vortex and the antivortex depends on the positive and negative value of the vortex winding numbers, respectively. The vortex winding number is Z v = c arg[∆(r)]ds, where c is a closed loop around the vortex center [244].…”

Section: A Vortex Bound State With Topologymentioning

confidence: 99%

Emergent vortex Majorana zero mode in iron-based superconductors

Kong¹,

Ding²

2020

Acta Phys. Sin.

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The vortex of iron-based superconductors is emerging as a promising platform for Majorana zero mode, owing to a magic integration among intrinsic vortex winding, non-trivial band topology, strong electron-electron correlations, high-Tc superconductivity and the simplification of single material. It overcomes many difficulties suffered in heterostructure-based Majorana platforms, including small topological gap, interfacial contamination, lattice imperfections, and etc. Isolated zero-bias peaks have been found in vortex of several iron-based superconductors. So far, studies from both experimental and theoretical aspects strongly indicate the realization of vortex Majorana zero mode, with a potential to be applied to fault-tolerant quantum computation. By taking Fe(Te,Se) superconductor as an example, here we review the original idea and research progress of Majorana zero modes in this new platform. After introducing the identifications of topological band structure and real zero modes in vortex, we summarize the physics behaviors of vortex Majorana zero modes systematically. First, relying on the behavior of the zero mode wave function and evidence of quasiparticle poisoning, we analyze the mechanism of emergence of vortex Majorana zero modes. Secondly, assisted with some well-established theories, we elaborate the measurements on "Majorana symmetry" and topological nature of vortex Majorana zero modes. After that, we switch from quantum physics to quantum engineering, and analyze the performance of vortex Majorana zero modes under real circumstances, which may potentially benefit the exploration of practical applications in the future. This review follows the physics properties of vortex Majorana zero modes, especially emphasizes the link between phenomena and mechanisms. It provides a chance to bridge the gap between the well-established theories and the newly discovered "iron home" of Majoranas.

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

Cited by 8 publications

References 54 publications

Topological superconductors: a review

Topological superconductors: a review

Condensation of fermion zero modes in the vortex

Emergent vortex Majorana zero mode in iron-based superconductors

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