Protected Helical Transport in Topological Insulators and Magnetically Doped Quantum Wires

目前的提案包含了对拓扑绝缘体和量子纳米线中受保护的螺旋传输的全面和详细的研究。理论研究的两个方向仍然是这一领域的关键，即：(I)提高对螺旋度保护弹道传输的稳健性的理解；(Ii)发展相互作用系统中螺旋相的先进理论。这些方向构成了当前提案的基础。这是项目(去掉符号)的直接延续和实质性扩展，由申请人指导的“一维电子与局部自旋耦合的对称保护输运：从拓扑绝缘体的边缘到半导体量子线”。这项新提议的灵感来自于最近产生的新科学想法和预期的与实验小组的密集合作。我们下一步的理论研究将包括三个方向：1)螺旋系统的一般理论(平衡外输运保护的稳健性；螺旋系统中Kondo/RKKY跃迁的数值研究；激发自旋态的慢弛豫-螺旋量子比特)；2)与磁性掺杂量子线中的HSS有关的基本理论问题(螺旋相的稳定性；各种导电通道；可能的任意子激发)；3)与清洁和掺杂铋线实验相关的理论问题(在SOI存在下的磁性掺杂线的相图，包括这种线中的非平凡自旋有序)；连接到超导引线的磁性掺杂导线中的螺旋相和Majorana边缘状态)。

The current proposal embraces a comprehensive and detailed study of protected helical transport in topological insulators and quantum nanowires. Two directions of the theoretical research remain pivotal is this field, namely: (i) improving understanding of the robustness of the helicity protected ballistic transport; and (ii) developing the advanced theory for the helical phases in the interacting systems. These directions form the basis of the current proposal. It is the immediate continuation and the substantial extension of the project (sign removed), ``Symmetry Protected Transport of 1D Electrons Coupled to Local Spins: from Edges of Topological Insulators to Semiconductor Quantum Wires'', directed by the applicant. The new proposal has been inspired by recently generated new scientific ideas and by a foreseen intensive collaboration with experimental groups. Next steps of our theoretical study will include three directions: 1) A general theory of the helical systems (robustness of the transport protection out of equilibrium; numerical study of the Kondo/RKKY transition in the helical systems; slow relaxation of excited spin states - helical qubits); 2) Fundamental theoretical questions related to the HSs in the magnetically doped quantum wires (stability of the helical phase; various conducting channels; possible anyonic excitations); 3) Theoretical questions related to experiments on clean and doped wires made of Bi (the phase diagram of the magnetically doped wires in the presence of SOI, including nontrivial spin orderings in such wires; helical phases and Majorana edge states in magnetically doped wires connected to superconducting leads).