Protected Helical Transport in Topological Insulators and Magnetically Doped Quantum Wires

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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).