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SUMMARY:Topological properties of Josephson current between two s- and p-w
 ave superconducting nanowires with Majorana fermions
DTSTART;VALUE=DATE-TIME:20201005T164500Z
DTEND;VALUE=DATE-TIME:20201005T170000Z
DTSTAMP;VALUE=DATE-TIME:20260916T183420Z
UID:indico-contribution-2144@cern.ch
DESCRIPTION:Speakers: Bahruz D. Suleymanli (National Research Nuclear Univ
 ersity MEPhI)\nJosephson current between two one-dimensional nanowires wit
 h proximity induced either s-wave or p-wave pairing and separated by a nar
 row dielectric barrier is calculated in the presence of Rashba spin-orbit 
 interaction (RSOI)\, in-plane and normal Zeeman magnetic fields (ZMF). A t
 opological superconducting phase in a Josephson junction of s-wave superco
 nductors (s-JJ) is realized under the condition $|∆|^2 > B^2 + h^2$\, wh
 ere Δ\, B\, and h are correspondingly the gap\, Zeeman energy of in-plane
  and normal magnetic fields. Instead\, the condition $∆_k = \\frac{\\vec
 {k}}{|k|}∆_0$ guarantees an existence of a conducting state in the gap a
 nd realization of a generic topological phase of the p-wave superconductor
  (p-JJ). Andreev retro-reflection is shown to be realized through two diff
 erent channels. A scattering in a conventional particle-hole channel\, whe
 n an electron-like quasi-particle reflects to a hole-like quasi-particle w
 ith opposite spins\, provides the current which depends only on the order 
 parameters’ phase differences ϕ\,  and oscillates fractionally with 4
 π period. Fractional oscillation of the current with 4π period is the ma
 in manifestation of realization of Majorana fermion in the system. Second 
 anomalous particle-hole channel\, corresponding to the Andreev reflection
  of an incident electron-like quasiparticle to hole-like quasiparticle wit
 h the same spin orientation\, survives only in the presence of the in-plan
 e magnetic field. The contribution of this channel to the Josephson curre
 nt oscillates with 4π period not only with ϕ but also with orientational
  angle of the in-plane magnetic field θ resulting in a magneto-Josephson
  effect. RSOI and ZMF are shown to split the quasi-electron and quasi-hol
 e excitation states in the superconducting gap\, and two quasi-particle an
 d quasi-hole pairs instead of one pair appear in the gap\, which are local
 ized symmetrically around Fermi level. ZMF is shown to destroy this symmet
 ry.  Even in the absence of the magnetic fields in s-JJ the energy gap be
 tween the Andreev bound states decreases with increasing RSOI. Investigati
 on of ac-Josephson current in s-JJ shows that the width of the resulting S
 hapiro steps in such a system can be tuned by varying the RSOI constant. I
 n the presence of RSOC and normal-to-plane magnetic field h in p-JJ\, a f
 orbidden gap is shown to open in the dependence of Andreev bound state ene
 rgies on the phases ϕ and θ at several values of RSOC strength and ZMF\,
  where Josephson current seems to vanish [1]. \n\nReferences:\n\n[1] E. Na
 khmedov\, B. D. Suleymanli et al.\, submitted to Phys. Rev. B (ArXiv: 1911
 .09289).\n\nhttps://indico.particle.mephi.ru/event/35/contributions/2144/
LOCATION:Discord Poster Server
URL:https://indico.particle.mephi.ru/event/35/contributions/2144/
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