TY - JOUR

T1 - Probability distribution of Majorana end-state energies in disordered wires

AU - Brouwer, Piet W.

AU - Duckheim, Mathias

AU - Romito, Alessandro

AU - Von Oppen, Felix

PY - 2011/11/1

Y1 - 2011/11/1

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevLett.107.196804

DO - 10.1103/PhysRevLett.107.196804

M3 - Journal article

AN - SCOPUS:80155171501

VL - 107

JO - Physical review letters

JF - Physical review letters

SN - 0031-9007

IS - 19

M1 - 196804

ER -