Brouwer, Piet W. and Duckheim, Mathias and Romito, Alessandro and Von Oppen, Felix
(2011)
*Probability distribution of Majorana end-state energies in disordered wires.*
Physical review letters, 107 (19): 196804.
ISSN 0031-9007

## 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 ε0 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 ε0 is log normal in the limit of large L, whereas the distribution of the lowest-lying bulk energy level ε1 has an algebraic tail at small ε1. Our findings have implications for the speed at which a topological quantum computer can be operated.