Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany.
Phys Rev Lett. 2011 Nov 4;107(19):196804. doi: 10.1103/PhysRevLett.107.196804. Epub 2011 Nov 1.
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 ε(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 ε(0) is log normal in the limit of large L, whereas the distribution of the lowest-lying bulk energy level ε(1) has an algebraic tail at small ε(1). Our findings have implications for the speed at which a topological quantum computer can be operated.
一维拓扑超导体在其末端存在马约拉纳束缚态。对于有限长度 L 的超导线，这些马约拉纳态组合成具有能量 ε(0)的费米子激发，其中 ε(0)在 L 中呈指数衰减。弱无序使能量分裂呈指数衰减，但会影响其典型值并导致大的样本间波动。我们表明，在大 L 的极限下，ε(0)的概率分布是对数正态的，而最低体能 ε(1)的分布在 ε(1)较小时具有幂律尾部。我们的发现对拓扑量子计算机的操作速度有影响。
