2016
DOI: 10.1103/physrevlett.116.237002
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Semiclassical Quantization of Spinning Quasiparticles in Ballistic Josephson Junctions

Abstract: A Josephson junction made of a generic magnetic material sandwiched between two conventional superconductors is studied in the ballistic semi-classic limit. The spectrum of Andreev bound states is obtained from the single-valuedness of a particle-hole spinor over closed orbits generated by electron-hole reflections at the interfaces between superconducting and normal materials. The semiclassical quantization condition is shown to depend only on the angle mismatch between initial and final spin directions along… Show more

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Cited by 13 publications
(15 citation statements)
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“…The general symmetries of the BdG Hamiltonian are well known [46]. In the quasiclassical limit, which is equivalent to the Andreev approximation [47], transport properties are determined by particles living exactly at the Fermi surface. In the BdG Hamiltonian this corresponds to the ξ = 0 case.…”
Section: Quasiclassical Symmetry Of the Charge Currentmentioning
confidence: 99%
“…The general symmetries of the BdG Hamiltonian are well known [46]. In the quasiclassical limit, which is equivalent to the Andreev approximation [47], transport properties are determined by particles living exactly at the Fermi surface. In the BdG Hamiltonian this corresponds to the ξ = 0 case.…”
Section: Quasiclassical Symmetry Of the Charge Currentmentioning
confidence: 99%
“…(10) can be generalized to the case of a spin-active weak link using the formalism developed in Ref. [37].…”
mentioning
confidence: 99%
“…Eq. 14 determines the spectrum of Andreev bound states (ABS) [9,10]. In a short junction, L ξ 0 , where ξ 0 ≡ v F /∆ is the superconducting coherence length, one obtains σ = ±∆ cos σΦ + ϕ 2 .…”
Section: One-dimensional Sfs Junctionmentioning
confidence: 99%
“…Ballistic SFS junctions have been widely explored in the past, mainly in two limiting cases. One of them is the semiclassical limit, in which the Fermi energy, µ, is assummed to be much larger than any other energy involved in the system, including the superconducting gap, ∆, and the Zeeman splitting, h [6][7][8][9][10]. In this limit, one can directly apply the Bohr-Sommerfeld semiclassical quantization condition [11] and demonstrate that, in the absence of interface barriers, the spectrum consists of two double-degenerate Andreev bound states with opposite energies.…”
Section: Introductionmentioning
confidence: 99%