Elementary-flux-pinning potential in type-II superconductors

Thuneberg, E. V.; Kurkijärvi, J.; Rainer, D.

doi:10.1103/physrevb.29.3913

Cited by 167 publications

(129 citation statements)

References 17 publications

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“…The quasiclassical transport equation (192) offers a more tractable way for studying microscopic structures of spatially inhomogeneous superfluids and superconductors, while it always contains an unphysical solution that is not normalizable [300]. Following Refs.…”

Section: Surface Andreev Bound States In the Quasiclassical Theorymentioning

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: Surface Andreev Bound States In the Quasiclassical Theorymentioning

confidence: 99%

Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

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“…(30), (32), (33), and (35). For the case of deflected trajectories we have to specify separately the momentumk ′ on L side andk on R side.…”

Section: B Propagatormentioning

confidence: 99%

Pinhole calculations of the Josephson effect in3He−B

Viljas¹,

Thuneberg

2002

Phys. Rev. B

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We study theoretically the dc Josephson effect between two volumes of superfluid 3 He-B. We first discuss how the calculation of the current-phase relationships is divided into a mesoscopic and a macroscopic problem. We then analyze mass and spin currents and the symmetry of weak links. In quantitative calculations the weak link is assumed to be a pinhole, whose size is small in comparison to the coherence length. We derive a quasiclassical expression for the coupling energy of a pinhole, allowing also for scattering in the hole. Using a selfconsistent order parameter near a wall, we calculate the current-phase relationships in several cases. In the isotextural case, the current-phase relations are plotted assuming a constant spin-orbit texture. In the opposite anisotextural case the texture changes as a function of the phase difference. For that we have to consider the stiffness of the macroscopic texture, and we also calculate some surface interaction parameters. We analyze the experiments by Marchenkov et al. We find that the observed π states and bistability hardly can be explained with the isotextural pinhole model, but a good quantitative agreement is achieved with the anisotextural model.

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“…The above expression of Ω sn is a simple extension of the weak-coupling BCS one [26,27]. We used the 15-points Gauss-Kronrod quadrature formula to integrate respect to s. We numerically confirmed that the self-energy for Matsubara-frequenciesΣ (iε n , α, r) can be decoupled asΣ…”

Section: Methodsmentioning

confidence: 70%