Protected Helical Transport in Topological Insulators and Magnetically Doped Quantum Wires

• Applicant: Dr. Oleg Yevtushenko
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2016 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 285941391

• Final Report Year: 2024

Final Report Abstract

Quantum technologies promise tremendous progress in electronics, computation, and communication. Their fundamental building blocks are protected quantum states which are able to provide error-free operation of quantum devices and their nanoelements. A famous representative of this family is helical states. They were discovered experimentally on edges of so-called topological insulators (TI) – insulators, whose bulk is in a topologically nontrivial state (1). The time-reversal symmetry (TRS) and the non-trivial topology of the TI bulk guarantee helicity (lock-in relation between spin and direction of propagation) of the gapless one-dimensional (1D) edge modes. Helicity prohibits elastic singleparticle backscattering by a spinless potential. Thus, at least in the absence of interactions, the helical modes are not liable to the effects of material imperfections, such as localization. In reality, the protection of the helical states in TI-based samples is not perfectly robust. Understanding possible mechanisms, which can lead to suppression of ballistic helical edge transport in TIs, attracted huge attention. Despite enormous efforts of researchers, a fully consistent theory explaining the suppression of helical transport in TIs in all experimental setups is still absent and remains a hot topic. This calls for a search for alternative platforms where the protected states, including helical ones, can be realized. Emergent helicity can originate in 1D wires with various interactions (2). A challenge is to find a flexible possibility for developing platforms which would allow one to maintain ballistic transport in rather long samples. The project addressed both the above-mentioned aspects of the theory of the helical low-dimensional systems, namely: 1) robustness of the helical protection on the TI edges, and 2) emergent helicity and related protection in magnetically doped wires. The latter systems are described by the seminal model of the Kondo- or Kondo-Heisenberg lattice (3). It includes itinerant electrons interacting with localized magnetic moments, named also Kondo spins. Apart from these main directions, several highly nontrivial phases and phase transitions were found in the magnetically doped TI edges and 1D wires. They encompassed a chiral lattice supersolid, a chiral spin liquid and an unusual transition between Kondo- and indirect exchange-dominated phases

Publications

• Quantum Phase Transition and Protected Ideal Transport in a Kondo Chain. Physical Review Letters, 115(21).
  Tsvelik, A. M. & Yevtushenko, O. M.
  
• Transport in helical Luttinger liquid with Kondo impurities. EPL (Europhysics Letters), 112(5), 57003.
  Yevtushenko, Oleg M.; Wugalter, Ari; Yudson, Vladimir I. & Altshuler, Boris L.
  
• Low energy properties of the Kondo chain in the RKKY regime. New Journal of Physics, 18(5), 053004.
  Schimmel, D. H.; Tsvelik, A. M. & Yevtushenko, O. M.
  
• Chiral Spin Order in Kondo-Heisenberg Systems. Physical Review Letters, 119(24).
  Tsvelik, A. M. & Yevtushenko, O. M.
  
• Chiral lattice supersolid on edges of quantum spin Hall samples. Physical Review B, 98(8).
  Yevtushenko, Oleg M. & Tsvelik, A. M.
  
• Kondo Impurities Coupled to a Helical Luttinger Liquid: RKKY-Kondo Physics Revisited. Physical Review Letters, 120(14).
  Yevtushenko, Oleg M. & Yudson, Vladimir I.
  
• Physics of arbitrarily doped Kondo lattices: From a commensurate insulator to a heavy Luttinger liquid and a protected helical metal. Physical Review B, 100(16).
  Tsvelik, A. M. & Yevtushenko, O. M.
  
• Protected helical transport in magnetically doped quantum wires: Beyond the one-dimensional paradigm. Physical Review B, 102(16).
  Stäbler, Florian; Tsvelik, Alexei M. & Yevtushenko, Oleg M.
  
• Transport in magnetically doped one-dimensional wires: can the helical protection emerge without the global helicity?. New Journal of Physics, 22(5), 053013.
  Tsvelik, A. M. & Yevtushenko, O. M.
  
• Suppression of ballistic helical transport by isotropic dynamical magnetic impurities. Physical Review B, 104(19).
  Yevtushenko, Oleg M. & Yudson, Vladimir I.
  
• Protection of edge transport in quantum spin Hall samples: spin-symmetry based general approach and examples. New Journal of Physics, 24(2), 023040.
  Yevtushenko, Oleg M. & Yudson, Vladimir I.
  
• RKKY to Kondo crossover in helical edge of a topological insulator. Physical Review Research, 5(3).
  Ferrer, Pol Alonso-Cuevillas; Yevtushenko, Oleg M. & Weichselbaum, Andreas