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Article overview
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Singularities of Andreev spectrum in multi-terminal Josephson junction | Tomohiro Yokoyama
; Yuli V. Nazarov
; | Date: |
1 Aug 2015 | Abstract: | The energies of Andreev bound states (ABS) forming in a $N$-terminal junction
are affected by $N - 1$ independent macroscopic phase differences between
superconducting leads and can be regarded as energy bands in $N - 1$ periodic
solid owing to the $2pi$ periodicity in all phases. We investigate the
singularities and peculiarities of the resulting ABS spectrum combining
phenomenological and analytical methods and illustrating with the numerical
results. We pay special attention on spin-orbit (SO) effects. We consider Weyl
singularities with a conical spectrum that are situated at zero energy in the
absence of SO interaction. We show that the SO interaction splits the spectrum
in spin like a Zeeman field would do. The singularity is preserved while
departed from zero energy. With SO interaction, points of zero-energy form an
$N - 2$ dimensional manifold in $N - 1$ dimensional space of phases, while this
dimension is $N - 3$ in the absence of SO interaction. The singularities of
other type are situated near the superconducting gap edge. In the absence
(presence) of SO interaction, the ABS spectrum at the gap edge is
mathematically analogues to that at zero energy in the presence (absence) of SO
interaction. We demonstrate that the gap edge touching (GET) points of the
spectrum in principle form $N - 2$ ($N - 3$) dimensional manifold when the SO
interaction is absent (present). Certain symmetry lines in the Brillouin zone
of the phases are exceptional from this rule, and GET there should be
considered separately. We derive and study the effective Hamiltonians for all
the singularities under consideration. | Source: | arXiv, 1508.0146 | Services: | Forum | Review | PDF | Favorites |
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