Erratum: Anomalous features of the proximity effect in triplet superconductors [Phys. Rev. B<b>72</b>, 140503(R) (2005)]

Tanaka, Y.; Asano, Yasuhiro; Golubov, A. A.; Kashiwaya, Satoshi

doi:10.1103/physrevb.73.059901

Cited by 45 publications

(78 citation statements)

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“…Nevertheless, OSO and OTE pair amplitudes can emerge ubiquitously in spatially non-uniform systems accompanied by Andreev bound states and anomalous proximity effect. In particular, anomalous charge and spin transport, electromagnetic responses, proximity effects via Andreev bound states have also been clarified in the light of odd-frequency Cooper pairing [306,307,308,309,310,311,312,313,314,315,316,317,318,319].…”

Section: Odd-frequency Pairing and Magnetizationmentioning

confidence: 99%

Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

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Abstract.Owing to the richness of symmetry and well-established knowledge on the bulk superfluidity, the superfluid 3 He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of 3 He in a multifaceted manner, including symmetry consideration, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the 3 He-B confined in a slab geometry. The 3 He-B under a magnetic field is separated to two different sub-phases: The symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered off by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnetic dipole interaction of 3 He nucleus. It is also demonstrated that odd-frequency evenparity Cooper pair amplitudes are emergent in low-lying quasiparticles. The key ingredients, symmetry protected Majorana fermions and odd-frequency pairing, bring an important consequence that the coupling of the surface states to an applied field is prohibited by the hidden discrete symmetry, while the topological phase transition with the spontaneous symmetry breaking is accompanied by anomalous enhancement and anisotropic quantum criticality of surface spin susceptibility. We also illustrate common topological features between topological crystalline superconductors and symmetry protected topological superfluids, taking UPt 3 and Rashba superconductors as examples.

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Section: Odd-frequency Pairing and Magnetizationmentioning

confidence: 99%

Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

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“…In a normal metal attached to a spin-singlet s-wave superconductor, penetrating Cooper pairs form the gap structure in the quasiparticle density of states (DOS) at the Fermi level (zero energy) and modify lowenergy properties there. In spin-triplet p-wave superconductor junctions, however, the penetrating Cooper pairs form a zeroenergy peak in the DOS [1][2][3]. This induces various anomalous electromagnetic properties in the normal metal [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

“…The energy dispersion of the topological edge states is flat as a function of the wave vector in the transverse direction (say k y ), which represents the high degree of the degeneracy in the zero-energy states (ZESs). The anomalous proximity effect stems from the penetration of such ZESs into the dirty normal metal while retaining their high degree of degeneracy [1,3,5]. Theoretically, it has been unclear what symmetry protects the high degeneracy of ZESs and why the perfect Andreev reflection persists at zero energy.…”

Section: Introductionmentioning

confidence: 99%

Anomalous proximity effect and theoretical design for its realization

2015

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We discuss the stability of zero-energy states appearing in a dirty normal metal attached to a superconducting thin film with Dresselhaus [110] spin-orbit coupling under an in-plane Zeeman field. The Dresselhaus superconductor preserves an additional chiral symmetry and traps more than one zero-energy state at its edges. All the zero-energy states at an edge belong to the same chirality in large Zeeman fields due to the effective p-wave pairing symmetry. The pure chiral nature of the wave function enables the zero-energy states to penetrate the dirty normal metal while retaining their high degree of degeneracy. We prove the perfect Andreev reflection into the dirty normal metal at zero energy.

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“…In our paper ballistic transport is assumed. If the ferromagnet becomes diffusive, we can expect anomalous proximity effect [53,[79][80][81][82][83] by odd-frequency spin-triplet s-wave pairing. Extension to this direction is also an interesting future study.…”

Section: Discussionmentioning

confidence: 99%

Josephson current in a normal-metal nanowire coupled to a superconductor/ferromagnet/superconductor junction

Ebisu

Taguchi

et al. 2016

Phys. Rev. B

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We consider a superconducting nanowire proximity coupled to a superconductor/ferromagnet/superconductor (S/F/S) junction, where the magnetization penetrates into a superconducting segment in a nanowire decaying as], where n is the site index and the ξ is the decay length. We tune chemical potential and spin-orbit coupling so that the topological superconducting regime hosting the Majorana fermion is realized for long ξ . We find that when ξ becomes shorter, zero energy state at the interface between a superconductor and a ferromagnet splits into two states at nonzero energy. Accordingly, the behavior of the Josephson current is drastically changed due to this "zero mode-nonzero mode crossover." By tuning the model parameters, we find an almost second-harmonic current-phase relation sin 2ϕ, where ϕ is the phase difference of the junction. Based on the analysis of Andreev bound state (ABS), we clarify that the current-phase relation is determined by coupling of the states within the energy gap. We find that the emergence of crossing points of ABS is a key ingredient to generate sin 2ϕ dependence in the current-phase relation. We further study both the energy and ϕ dependence of pair amplitudes in the ferromagnetic region. For large ξ , an odd-frequency spin-triplet s-wave component is dominant. The magnitude of the odd-frequency pair amplitude is enhanced at the energy level of ABS.

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Erratum: Anomalous features of the proximity effect in triplet superconductors [Phys. Rev. B72, 140503(R) (2005)]

Cited by 45 publications

References 0 publications

Symmetry protected topological superfluid³He-B

Symmetry protected topological superfluid³He-B

Anomalous proximity effect and theoretical design for its realization

Josephson current in a normal-metal nanowire coupled to a superconductor/ferromagnet/superconductor junction

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Erratum: Anomalous features of the proximity effect in triplet superconductors [Phys. Rev. B72, 140503(R) (2005)]

Cited by 45 publications

References 0 publications

Symmetry protected topological superfluid3He-B

Symmetry protected topological superfluid3He-B

Anomalous proximity effect and theoretical design for its realization

Josephson current in a normal-metal nanowire coupled to a superconductor/ferromagnet/superconductor junction

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Symmetry protected topological superfluid³He-B

Symmetry protected topological superfluid³He-B