On the derivation of quasiclassical equations for superconductors

Shelankov, A. L.

doi:10.1007/bf00681651

Cited by 124 publications

(87 citation statements)

References 6 publications

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“…To obtain a unique solution for g, Eq. (192) must be supplemented by the normalization condition on the quasiclassical propagator as [294,298,299] g(k, r; ω n )…”

Section: 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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“…To obtain a unique solution for g, Eq. (192) must be supplemented by the normalization condition on the quasiclassical propagator as [294,298,299] g(k, r; ω n )…”

Section: Quasiclassical Theorymentioning

confidence: 99%

Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

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“…[23][24][25] For specular scattering where an in-going trajectory is scattered into one outgoing direction the boundary condition for the Eilenberger equation reads 25…”

Section: Spin Dynamics In Finite Systemsmentioning

confidence: 99%

Spin relaxation in narrow wires of a two-dimensional electron gas

et al. 2006

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How does an initially homogeneous spin polarization in a confined two-dimensional electron gas with Rashba spin-orbit coupling evolve in time? How does the relaxation time depend on system size? We study these questions for systems of a size that is much larger than the Fermi wavelength, but comparable and even shorter than the spin relaxation length. Depending on the confinement spin relaxation may become faster or slower than in the bulk. An initially homogeneously polarized spin system evolves into a spiral pattern.

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“…Next, one treats the interaction Hamiltonian as an insertion in the self-energy, which leads to a new set of semi-classical Gor'kov equations. These equations are still too complicated to use effectively, but they can be simplified to the so-called Eilenberger equations [9,[13][14][15] (at the expense of losing detailed information about excitations) by introducing the energy-integrated Green functions,…”

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confidence: 99%

Enhancing superconductivity: Magnetic impurities and their quenching by magnetic fields

Wei¹,

Pekker²,

Rogachev³

et al. 2006

Europhys. Lett.

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Abstract. -Magnetic fields and magnetic impurities are each known to suppress superconductivity. However, as the field quenches (i.e. polarizes) the impurities, rich consequences, including field-enhanced superconductivity, can emerge when both effects are present. For the case of superconducting wires and thin films, this field-spin interplay is investigated via the Eilenberger-Usadel scheme. Non-monotonic dependence of the critical current on the field (and therefore field-enhanced superconductivity) is found to be possible, even in parameter regimes in which the critical temperature decreases monotonically with increasing field. The present work complements that of Kharitonov and Feigel'man, which predicts non-monotonic behavior of the critical temperature.

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On the derivation of quasiclassical equations for superconductors

Cited by 124 publications

References 6 publications

Symmetry protected topological superfluid³He-B

Symmetry protected topological superfluid³He-B

Spin relaxation in narrow wires of a two-dimensional electron gas

Enhancing superconductivity: Magnetic impurities and their quenching by magnetic fields

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On the derivation of quasiclassical equations for superconductors

Cited by 124 publications

References 6 publications

Symmetry protected topological superfluid3He-B

Symmetry protected topological superfluid3He-B

Spin relaxation in narrow wires of a two-dimensional electron gas

Enhancing superconductivity: Magnetic impurities and their quenching by magnetic fields

Contact Info

Product

Resources

About

Symmetry protected topological superfluid³He-B

Symmetry protected topological superfluid³He-B