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Majorana fermions in finite-size strips with in-plane magnetic fields

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  • Vardan Kaladzhyan

    (Institut de Physique Théorique, CEA/Saclay, Orme des Merisiers
    Laboratoire de Physique des Solides, CNRS, Univ. Paris-Sud, Université Paris-Saclay)

  • Julien Despres

    (Institut de Physique Théorique, CEA/Saclay, Orme des Merisiers
    Laboratoire Charles Fabry, Institut d’Optique, CNRS, Univ. Paris-Saclay)

  • Ipsita Mandal

    (University of Basel)

  • Cristina Bena

    (Institut de Physique Théorique, CEA/Saclay, Orme des Merisiers
    Laboratoire de Physique des Solides, CNRS, Univ. Paris-Sud, Université Paris-Saclay)

Abstract

We study the Majorana bound states (MBS) arising in finite-size strips with Rashba spin-orbit coupling in the presence of an in-plane Zeeman magnetic field. Using two different methods, first, the numerical diagonalization of the tight-binding Hamiltonian, and second, finding the singular points of the Hamiltonian [I. Mandal, Europhys. Lett. 110, 67005 (2015); I. Mandal, S. Tewari, Physica E 79, 180 (2016); I. Mandal, Condens. Matter Phys. 19, 33703 (2016); P. San-Jose, E. Prada, R. Aguado, Sci. Rep. 6, 21427 (2016)], we obtain the topological phase diagram for these systems as a function of the chemical potential and the magnetic field, and we demonstrate the consistency of these two methods. By introducing disorder into these systems we confirm that the states with even number of Majorana pairs are not topologically protected. Finally, we show that a calculation of the ℤ2 topological invariants recovers correctly the parity of the number of MBS pairs, and it is thus fully consistent with the phase diagrams of the disordered systems.

Suggested Citation

  • Vardan Kaladzhyan & Julien Despres & Ipsita Mandal & Cristina Bena, 2017. "Majorana fermions in finite-size strips with in-plane magnetic fields," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(11), pages 1-9, November.
    • Handle: RePEc:spr:eurphb:v:90:y:2017:i:11:d:10.1140_epjb_e2017-80103-y
    DOI: 10.1140/epjb/e2017-80103-y
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    Mesoscopic and Nanoscale Systems;

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