Description
Zeeman fields can drive semiconductor quantum wires with
strong spin-orbit coupling and in proximity to s-wave
superconductors into a topological phase which supports end
Majorana fermions and offers an attractive platform for
realizing topological quantum information processing [1,2].
In this talk, I discuss how potential disorder affects the
topological phase by a combination of analytical and
numerical approaches. We find that the robustness of the
topological phase against disorder depends sensitively and
non-monotonously on the Zeeman field applied to the wire
[3]. We also obtain the entire distribution function of the
energy of the Majorana end states as well as of the lowest
bulk state in wires of finite length, and discuss the
implications for the speed at which a hypothetical
topological quantum computer can be operated [4].
[1] Y. Oreg, G. Refael, F. von Oppen, Helical liquids and
Majorana bound states in quantum wires, Phys. Rev. Lett.
105, 177002 (2010)
[2] J. Alicea, Y. Oreg, G. Refael, F. von Oppen, M.P.A.
Fisher, Non-Abelian statistics and topological quantum
computation in 1D wire networks, Nature Physics 7, 412 (2011)
[3] P. W. Brouwer, M. Duckheim, A. Romito, F. von Oppen,
Topological superconducting phases in disordered quantum
wires with strong spin-orbit coupling, arXiv:1103.2746
[4] P. W. Brouwer, M. Duckheim, A. Romito, F. von Oppen,
Probability distribution of Majorana end state energies in
disordered wires, arXiv:1104.1531.
