https://doi.org/10.1140/epjb/e2017-80103-y
Regular Article
Majorana fermions in finite-size strips with in-plane magnetic fields
1
Institut de Physique Théorique, CEA/Saclay, Orme des Merisiers,
91190
Gif-sur-Yvette Cedex, France
2
Laboratoire de Physique des Solides, CNRS, Univ. Paris-Sud, Université Paris-Saclay,
91405
Orsay Cedex, France
3
Laboratoire Charles Fabry, Institut d’Optique, CNRS, Univ. Paris-Saclay,
2 avenue Augustin Fresnel,
91127
Palaiseau Cedex, France
4
Department of Physics, University of Basel,
Klingelbergstrasse 82,
CH-4056
Basel, Switzerland
a e-mail: vardan.kaladzhyan@cea.fr
Received:
20
February
2017
Received in final form:
19
June
2017
Published online: 7
November
2017
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.
Key words: Mesoscopic and Nanoscale Systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2017