Probability distribution of Majorana end-state energies in disordered wires

2011/04/08 by Piet W. Brouwer, Mathias Duckheim, Alessandro Romito +1 · 2 citations
Physics and Astronomy · #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevlett.107.196804

4 pages, 2 figures

arxiv created 2011/04/08 · arxiv updated 2015/05/27

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.

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