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Probability distribution of Majorana end-state energies in disordered wires
Phys. Rev. Lett. 107, 196804 (2011) (pdf) ; arXiv:1104.1531v1 [cond-mat.mes-hall]
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 $\varepsilon_0$ 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 $\varepsilon_0$ is log normal in the limit of large $L$, whereas the distribution of the lowest-lying bulk energy level $\varepsilon_1$ has an algebraic tail at small $\varepsilon_1$. Our findings have implications for the speed at which a topological quantum computer can be operated.
Topological superconducting phases in disordered quantum wires with strong spin-orbit coupling
Phys. Rev. B 84, 144526 (2011) (pdf); arXiv:1103.2746v1 [cond-mat.mes-hall]
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. Here, we investigate how potential disorder affects the topological phase by a combination of analytical and numerical approaches. Most prominently, we find that the robustness of the topological phase against disorder depends sensitively and non-monotonously on the Zeeman field applied to the wire.
Andreev reflection from non-centrosymmetric superconductors and Majorana bound state generation in half-metallic ferromagnets