title: Probability distribution of Majorana end-state energies in disordered wires.
abstract: One-dimensional topological superconductors harbor Majorana bound states at their ends. For superconducting wires of finite length L, these Majorana states combine into fermionic excitations with an energy ε(0) that is exponentially small in L. Weak disorder leaves the energy splitting exponentially small, but affects its typical value and causes large sample-to-sample fluctuations. We show that the probability distribution of ε(0) is log normal in the limit of large L, whereas the distribution of the lowest-lying bulk energy level ε(1) has an algebraic tail at small ε(1). Our findings have implications for the speed at which a topological quantum computer can be operated.
authors.affiliation: Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: Piet W
authors.initials: PW
authors.lastname: Brouwer
authors.forename: Mathias
authors.initials: M
authors.lastname: Duckheim
authors.forename: Alessandro
authors.initials: A
authors.lastname: Romito
authors.forename: Felix
authors.initials: F
authors.lastname: von Oppen