Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling

We consider two coupled time-reversal-invariant helical edge modes of the same helicity, such as would occur on two stacked quantum spin Hall insulators. In the presence of interaction, the low-energy physics is described by two collective modes, one corresponding to the total current flowing around the edge and the other one describing relative fluctuations between the two edges. We find that quite generically, the relative mode becomes gapped at low temperatures, but only when tunneling between the two helical modes is nonzero. There are two distinct possibilities for the gapped state depending on the relative size of different interactions. If the intraedge interaction is stronger than the interedge interaction, the state is characterized as a spin-nematic phase. However, in the opposite limit, when the interaction between the helical edge modes is strong compared to the interaction within each mode, a spin-density wave forms, with emergent topological properties. First, the gap protects the conducting phase against localization by weak nonmagnetic impurities; second, the protected phase hosts localized zero modes on the ends of the edge that may be created by sufficiently strong nonmagnetic impurities.

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“…This discussion is then analogous to the one presented in [34,35] for the case of nonhelical chains. These impurities are modeled by…”

Section: Boundary Zero Modes In the Protected Phasementioning

confidence: 71%

Phase diagram of two interacting helical states

2016

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“…[20] putting the model in the class DIII, which is a Z 2 topological insulator in one dimension; the latter was applied in Ref. [19] putting the model in the class BDI which has a Z topological index.…”

Section: Discussionmentioning

confidence: 99%

Interaction induced topological protection in one‐dimensional conductors

Kainaris

Santos

Gutman

et al. 2017

Fortschritte der Physik

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We discuss two one-dimensional model systems -the first is a single channel quantum wire with Ising anisotropy, while the second is two coupled helical edge states. We show that the two models are governed by the same low energy effective field theory, and interactions drive both systems to exhibit phases which are metallic, but with all single particle excitations gapped. We show that such states may be either topological or trivial; in the former case, the system demonstrates gapless end states, and insensitivity to disorder.

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“…(4) from the beginning, and simply use the transformed Hamiltonian H , as we would expect for non-interacting electrons. Note that deviations of the spectrum from the parabolic form occur at higher orders in (g/Ω), 25,26,34 but they are not important for our analysis.…”

Section: Modelmentioning

confidence: 98%

Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields

et al. 2016

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A partially gapped spectrum due to the application of a magnetic field is one of the main probes of Rashba spin-orbit coupling in nanowires. Such a "helical gap" manifests itself in the linear conductance, as well as in dynamic response functions such as the spectral function, the structure factor, or the tunnelling density of states. In this paper, we investigate theoretically the signature of the helical gap in these observables with a particular focus on the interplay between Rashba spin-orbit coupling and electron-electron interactions. We show that in a quasi-one-dimensional wire, interactions can open a helical gap even without magnetic field. We calculate the dynamic response functions using bosonization, a renormalization group analysis, and the exact form factors of the emerging sine-Gordon model. For special interaction strengths, we verify our results by refermionization. We show how the two types of helical gaps, caused by magnetic fields or interactions, can be distinguished in experiments.

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Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling

Cited by 47 publications

References 43 publications

Phase diagram of two interacting helical states

Phase diagram of two interacting helical states

Interaction induced topological protection in one‐dimensional conductors

Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields

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