Robustness of Majorana Modes and Minigaps in a Spin-Orbit-Coupled Semiconductor-Superconductor Heterostructure

We study the robustness of Majorana zero energy modes and minigaps of quasiparticle excitations in a vortex by numerically solving Bogoliubov-deGennes equations in a heterostructure composed of an \textit{s} -wave superconductor, a spin-orbit-coupled semiconductor thin film, and a magnetic insulator. This heterostructure was proposed recently as a platform for observing non-Abelian statistics and performing topological quantum computation. The dependence of the Majorana zero energy states and the minigaps on various physics parameters (Zeeman field, chemical potential, spin-orbit coupling strength) is characterized. We find the minigaps depend strongly on the spin-orbit coupling strength. In certain parameter region, the minigaps are linearly proportional to the \textit{s}-wave superconducting pairing gap $\Delta_{s}$, which is very different from the $\Delta_{s}^{2}$ dependence in a regular \textit{s-} or \textit{\p}-wave superconductor. We characterize the zero energy chiral edge state at the boundary and calculate the STM signal in the vortex core that shows a pronounced zero energy peak. We show that the Majorana zero energy states are robust in the presence of various types of impurities. We find the existence of impurity potential may increase the minigaps and thus benefit topological quantum computation.Comment: 11 pages, 15 figure

Quantum transport in a curved one-dimensional quantum wire with spin-orbit interactions

The one-dimensional effective Hamiltonian for a planar curvilinear quantum wire with arbitrary shape is proposed in the presence of the Rashba spin-orbit interaction. Single electron propagation through a device of two straight lines conjugated with an arc has been investigated and the analytic expressions of the reflection and transmission probabilities have been derived. The effects of the device geometry and the spin-orbit coupling strength $\alpha$ on the reflection and transmission probabilities and the conductance are investigated in the case of spin polarized electron incidence. We find that no spin-flip exists in the reflection of the first junction. The reflection probabilities are mainly influenced by the arc angle and the radius, while the transmission probabilities are affected by both spin-orbit coupling and the device geometry. The probabilities and the conductance take the general behavior of oscillation versus the device geometry parameters and $\alpha$. Especially the electron transportation varies periodically versus the arc angle $\theta_{w}$. We also investigate the relationship between the conductance and the electron energy, and find that electron resonant transmission occurs for certain energy. Finally, the electron transmission for the incoming electron with arbitrary state is considered. For the outgoing electron, the polarization ratio is obtained and the effects of the incoming electron state are discussed. We find that the outgoing electron state can be spin polarization and reveal the polarized conditions.Comment: 7 pages, 8 figure

Protein Evolution in Yeast Transcription Factor Subnetworks

When averaged over the full yeast protein–protein interaction and transcriptional regulatory networks, protein hubs with many interaction partners or regulators tend to evolve significantly more slowly due to increased negative selection. However, genome-wide analysis of protein evolution in the subnetworks of associations involving yeast transcription factors (TFs) reveals that TF hubs do not tend to evolve significantly more slowly than TF non-hubs. This result holds for all four major types of TF hubs: interaction hubs, regulatory in-degree and out-degree hubs, as well as co-regulatory hubs that jointly regulate target genes with many TFs. Furthermore, TF regulatory in-degree hubs tend to evolve significantly more quickly than TF non-hubs. Most importantly, the correlations between evolutionary rate (KA/KS) and degrees for TFs are significantly more positive than those for generic proteins within the same global protein–protein interaction and transcriptional regulatory networks. Compared to generic protein hubs, TF hubs operate at a higher level in the hierarchical structure of cellular networks, and hence experience additional evolutionary forces (relaxed negative selection or positive selection through network rewiring). The striking difference between the evolution of TF hubs and generic protein hubs demonstrates that components within the same global network can be governed by distinct organizational and evolutionary principles.National Natural Science Foundation of China (10801131, 10631070); National Science Foundation (DGE-0654108); Pharmaceutical Research and Manufacturers of America Foundation (Research Starter Grant in Informatics); K. C. Wong Education Foundatio