Testing the formation of Majorana states using Majorana polarization

Cristina Bena (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We study the formation of Majorana states in superconductors using Majorana polarization, which can locally evaluate the Majorana character of a given state. We introduce the definition of the Majorana polarization vector and of the corresponding criterion to identify a Majorana state, and we apply it to some simple cases such as a one-dimensional wire with spin-orbit coupling, subject to a Zeeman magnetic field, and proximitized by a superconductor, as well as to an NS junction made with such a wire. We also apply this criterion to two-dimensional finite-size strips and squares subject to the same physical conditions. Our analysis demonstrates the necessity of using the Majorana polarization local order parameter to characterize the Majorana states, particularly in finite-size systems.

Keywords: Majorana fermions; Edge state; Topological superconductors; Fermions de Majorana; États de bord; Supraconducteurs topologiques

Domains: Superconductivity [cond-mat.supr-con]; General Physics [physics.gen-ph]

Cristina Bena. Testing the formation of Majorana states using Majorana polarization. Comptes Rendus Physique, 2017, 18, pp.349-357. ⟨10.1016/j.crhy.2017.09.005⟩. ⟨cea-01626937⟩