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Resilience of Majorana Fermions in 2XY Chain in the Presence of Disorder

Habibi, Alireza | 2018

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51338 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rouhani, Shahin; Jafari, Akbar
  7. Abstract:
  8. In this thesis, we investigate the effect of disorder on Majorana fermions at the boundary of one-dimensional topological superconductor. Starting from one-dimensional spin model nXY and then applying the Jordan-Wigner transformation result in one-dimensional topological superconductor. The Majorana fermions are found in the topological superconductor boundaries, protected by particle-hole and time-reversal symmetries. On the other hand, these fermions are highly localized at the boundary. Owing to non-trivial topology, the Majorana fermions are not affected by weak disorder. Increasing the disorder strength, the localization length of the Majorana fermions increases. Upon further increase in disorder strength, at a threshold disorder, the Majorana end modes overlap and annihilate each other. By means of winding number in real space, we examine the topology of the system. Consequently, we show that in topologically transition points the localization length of the system diverges. Having more than one pair of Majorana fermions, each pair annihilates at different threshold disorders. Furthermore, by breaking the time reversal symmetry, Majorana fermions present different behaviors against the disorder which is examined in details in this thesis. Our results have concentrated on special case n=2 in this resent thesis
  9. Keywords:
  10. Topological Insulator ; Majorana Fermion ; Kitaev Model ; Anderson Localization ; P-Wave Holographic Superconductor ; 2XY Chain

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