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Protection of Edge transport in Quantum Spin Hall samples: Spin-Symmetry Based General Approach and Examples
Mesoscale and Nanoscale Physics · Submitted 18 Sep 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We systematize various theories of helical transport with the help of the spin conservation analysis which allows one to single out setups with the ballistic conductance being robustly protected regardless of the electron backscattering.
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The abstract, sentence by sentence
Understanding possible mechanisms, which can lead to suppression of helical edge transport in Quantum Spin Hall (QSH) systems, attracted huge attention right after the first experiments revealing the fragility of the ballistic conductance. Despite the very intensive research and the abundance of theoretical models, the fully consistent explanation of the experimental results is still lacking. We systematize various theories of helical transport with the help of the spin conservation analysis which allows one to single out setups with the ballistic conductance being robustly protected regardless of the electron backscattering. First, we briefly review different theories of edge transport in the QSH samples with and without the spin axial symmetry of the electrons including those theoretical predictions which are not consistent with the spin conservation analysis and, thus, call for a deeper study. Next, we illustrate the general approach by a detailed study of representative examples. One of them addresses the helical edge coupled to an array of Heisenberg-interacting magnetic impurities (MIs) and demonstrates that the conductance remains ballistic even if the time-reversal symmetry on the edge is (locally) broken but the total spin is conserved. Another example focuses on the effects of the space-fluctuating spin-orbit interaction on the QSH edge. It reveals weakness of the protection in several cases, including, e.g., the presence of either the U(1)-symmetric, though not fully isotropic, MIs or generic electron-electron interactions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Understanding possible mechanisms, which can lead to suppression of helical edge transport in Quantum Spin Hall (QSH) systems, attracted huge attention right after the first experiments revealing the fragility of the ballistic conductance. | background 1.00 | 0.04 | 0.02 | asserted 0.85 |
| s1 | Despite the very intensive research and the abundance of theoretical models, the fully consistent explanation of the experimental results is still lacking. | gap 0.98 | 0.05 | 0.02 | asserted 1.00 |
| s2 | We systematize various theories of helical transport with the help of the spin conservation analysis which allows one to single out setups with the ballistic conductance being robustly protected regardless of the electron backscattering. | contribution 0.93 | 0.91 | 0.72 | asserted 0.98 |
| s3 | First, we briefly review different theories of edge transport in the QSH samples with and without the spin axial symmetry of the electrons including those theoretical predictions which are not consistent with the spin conservation analysis and, thus, call for a deeper study. | contribution 0.63 | 0.48 | 0.05 | asserted 0.83 |
| s4 | Next, we illustrate the general approach by a detailed study of representative examples. | contribution 0.54 | 0.78 | 0.03 | asserted 0.74 |
| s5 | One of them addresses the helical edge coupled to an array of Heisenberg-interacting magnetic impurities (MIs) and demonstrates that the conductance remains ballistic even if the time-reversal symmetry on the edge is (locally) broken but the total spin is conserved. | result 0.77 | 0.85 | 0.31 | asserted 1.00 |
| s6 | Another example focuses on the effects of the space-fluctuating spin-orbit interaction on the QSH edge. | contribution 0.96 | 0.65 | 0.03 | unclear 0.57 |
| s7 | It reveals weakness of the protection in several cases, including, e.g., the presence of either the U(1)-symmetric, though not fully isotropic, MIs or generic electron-electron interactions. | result 0.99 | 0.82 | 0.12 | asserted 0.97 |
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The paper
Original abstract
Understanding possible mechanisms, which can lead to suppression of helical edge transport in Quantum Spin Hall (QSH) systems, attracted huge attention right after the first experiments revealing the fragility of the ballistic conductance. Despite the very intensive research and the abundance of theoretical models, the fully consistent explanation of the experimental results is still lacking. We systematize various theories of helical transport with the help of the spin conservation analysis which allows one to single out setups with the ballistic conductance being robustly protected regardless of the electron backscattering. First, we briefly review different theories of edge transport in the QSH samples with and without the spin axial symmetry of the electrons including those theoretical predictions which are not consistent with the spin conservation analysis and, thus, call for a deeper study. Next, we illustrate the general approach by a detailed study of representative examples. One of them addresses the helical edge coupled to an array of Heisenberg-interacting magnetic impurities (MIs) and demonstrates that the conductance remains ballistic even if the time-reversal symmetry on the edge is (locally) broken but the total spin is conserved. Another example focuses on the effects of the space-fluctuating spin-orbit interaction on the QSH edge. It reveals weakness of the protection in several cases, including, e.g., the presence of either the U(1)-symmetric, though not fully isotropic, MIs or generic electron-electron interactions.
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How the literature uses it
4 arXiv papers cite this in 5 sentences
Papers citing it · 4 sentences without a confident label
Cites it as background 1 paper
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At low energies, interacting electrons on the QSH edge are described by the Luttinger Hamiltonian [ref] [equation] Here, we have for simplicity neglected possible bulk Rashba spin-orbit interaction that induces spin rotation in chiral channels (for the discussion of effects of this rotation on transport in helical edges, see, e.g., Refs. [ref] ).
Does delta-$T$ noise probe quantum statistics? · Setups and Models · 0.84
What it cites · 2 sentences without a confident label
Cites as background 2 papers
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Helical transport originates on edges of time-reversal invariant two-dimensional topological insulators, the so-called Quantum Spin Hall (QSH) samples [ref] which attract an enormous and continuous attention of experimentalists [ref] and theoreticians [ref] during past decade.
Tomonaga-Luttinger liquid in the edge channels of a quantum spin Hall insulator · Introduction · 1.00
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Helical transport originates on edges of time-reversal invariant two-dimensional topological insulators, the so-called Quantum Spin Hall (QSH) samples [ref] which attract an enormous and continuous attention of experimentalists [ref] and theoreticians [ref] during past decade.
Topological phase transition in quantum spin Hall insulator in the presence of charge lattice coupling · Introduction · 1.00
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