Vortices in chiral, spin-triplet superconductors and superfluids

Sauls, J. A.; Eschrig, Matthias

doi:10.1088/1367-2630/11/7/075008

Cited by 70 publications

(90 citation statements)

References 66 publications

(97 reference statements)

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“…Here the 2 center-of-mass angular momentum of the vortex can be transferred into the orbital angular momentum of the chiral d-wave state and the d-wave state can thus appear in the vortex core [148,149,150]. By this process the intrinsic chiral d-wave state in graphene has been shown to be significantly strengthened in the core of a doubly quantized s-wave superconducting vortex [151].…”

Section: Superconducting Proximity Effectsmentioning

confidence: 99%

Chirald-wave superconductivity in doped graphene

Black‐Schaffer

Honerkamp

2014

J. Phys.: Condens. Matter

175

176

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Abstract. A highly unconventional superconducting state with a spin-singlet d x 2 −y 2 ± id xy -wave, or chiral d-wave, symmetry has recently been proposed to emerge from electron-electron interactions in doped graphene. Especially graphene doped to the van Hove singularity at 1/4 doping, where the density of states diverges, has been argued to likely be a chiral d-wave superconductor. In this review we summarize the currently mounting theoretical evidence for the existence of a chiral d-wave superconducting state in graphene, obtained with methods ranging from mean-field studies of effective Hamiltonians to angle-resolved renormalization group calculations. We further discuss multiple distinctive properties of the chiral d-wave superconducting state in graphene, as well as its stability in the presence of disorder. We also review means of enhancing the chiral d-wave state using proximity-induced superconductivity. The appearance of chiral d-wave superconductivity is intimately linked to the hexagonal crystal lattice and we also offer a brief overview of other materials which have also been proposed to be chiral d-wave superconductors.

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Section: Superconducting Proximity Effectsmentioning

confidence: 99%

Chirald-wave superconductivity in doped graphene

Black‐Schaffer

Honerkamp

2014

J. Phys.: Condens. Matter

175

176

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“…37,38 In addition, the appearance of unconventional pair amplitudes in vortices has attracted great interest in general. [30][31][32][33][34] For this reason we here also provide a detailed investigation of the superconducting pair amplitude…”

Section: Pair Amplitudesmentioning

confidence: 99%

Probing vortex Majorana fermions and topology in semiconductor/superconductor heterostructures

Björnson

Black‐Schaffer

2015

Phys. Rev. B

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We investigate the local density of states, spectral function, and superconducting pair amplitudes for signatures of Majorana fermions in vortex cores in ferromagnetic and spin-orbit coupled semiconductorsuperconductor heterostructures. We show that the Majorana fermion quasiparticle momentum distribution is always symmetrically distributed at a finite radius around a high symmetry point, thereby providing a necessary condition for a low-energy state to be a Majorana fermion. In real space profiles of the local density of states through the vortex core the Majorana fermion, together with other finite-energy vortex states, form a characteristic x-shape structure only present at non-trivial topology. Moreover, we find that the Mexican hat band structure property of the topologically non-trivial phase translates into multiple high-intensity band edges and also vortex core states located above the superconducting gap in the local density of states. Finally, we find no strong correlation between odd-frequency pairing and the appearance of Majorana fermions, but odd-frequency pairing exists as soon as ferromagnetism is present. In fact, we find that the only vortex superconducting pair amplitude directly related to any phase transition, is the appearance of certain spin-triplet p-wave pairing components in the vortex core at a pre-topological vortex core widening transition.

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“…We start with the quasi-classical spinful Eilenberger equation [50][51][52][53][54]. The quasi-classical Green's function g(k, r, ω n ) is calculated using the Eilenberger equation…”

Section: Quasi-classical Eilenberger Theorymentioning

confidence: 99%

A Spin Triplet Superconductor UPt₃

et al. 2012

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Motivated by a recent angle-resolved thermal conductivity experiment that shows a twofold gap symmetry in the high-field and low-temperature C phase in the heavy-fermion superconductor UPt3, we group-theoretically identify the pairing functions as E1u with the f -wave character for all the three phases. The pairing functions are consistent with the observation as well as with a variety of existing measurements. By using a microscopic quasi-classical Eilenberger equation with the identified triplet pairing function under applied fields, we performed detailed studies of the vortex structures for three phases, including the vortex lattice symmetry, the local density of states, and the internal field distribution. These quantities are directly measurable experimentally by SANS, STM/STS, and NMR, respectively. It is found that, in the B phase of low H and low T , the double-core vortex is stabilized over a singular vortex. In the C phase, thermal conductivity data are analyzed to confirm the gap structure proposed. We also give detailed comparisons of various proposed pair functions, concluding that the present scenario of E1u with the f -wave, which is an analogue to the triplet planar state, is better than the E2u or E1g scenario. Finally, we discuss the surface topological aspects of Majorana modes associated with the E f 1u state of planar like features.

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Vortices in chiral, spin-triplet superconductors and superfluids

Cited by 70 publications

References 66 publications

Chirald-wave superconductivity in doped graphene

Chirald-wave superconductivity in doped graphene

Probing vortex Majorana fermions and topology in semiconductor/superconductor heterostructures

A Spin Triplet Superconductor UPt₃

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Vortices in chiral, spin-triplet superconductors and superfluids

Cited by 70 publications

References 66 publications

Chirald-wave superconductivity in doped graphene

Chirald-wave superconductivity in doped graphene

Probing vortex Majorana fermions and topology in semiconductor/superconductor heterostructures

A Spin Triplet Superconductor UPt3

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A Spin Triplet Superconductor UPt₃