Anderson localization of a Majorana fermion

¹ Institute for Theoretical Physics, ETH Zürich - 8093 Zürich, Switzerland
² Institute for Theoretical Physics, University of Zürich - 8057 Zürich, Switzerland
³ Max Planck Institute for Solid State Research - Heisenbergstr. 1, 70569 Stuttgart, Germany
⁴ L. D. Landau Institute for Theoretical Physics - 142432 Chernogolovka, Russia
⁵ Moscow Institute of Physics and Technology - 141700 Moscow, Russia

Received: 24 January 2014
Accepted: 16 April 2014

Abstract

Isolated Majorana fermion states can be produced at the boundary of a topological superconductor in a quasi–one-dimensional geometry. If such a superconductor is connected to a disordered quantum wire, the Majorana fermion is spread into the wire, subject to Anderson localization. We study this effect in the limit of a thick wire with broken time-reversal and spin-rotational symmetries. With the use of a supersymmetric nonlinear sigma model, we calculate the average local density of states in the wire as a function of energy and of the distance from the interface with the superconductor. Our results may be qualitatively explained by the repulsion of states from the Majorana level and by Mott hybridization of localized states.