Interaction induced topological protection in one‐dimensional conductors

We develop a framework to analyze one-dimensional topological superconductors with charge conservation. In particular, we consider models with N flavors of fermions and (Z2) N symmetry, associated with the conservation of the fermionic parity of each flavor. For a single flavor, we recover the result that a distinct topological phase with exponentially localized zero modes does not exist due to absence of a gap to single particles in the bulk. For N > 1, however, we show that the ends of the system can host low-energy, exponentially-localized modes. The analysis can readily be generalized to systems in other symmetry classes. To illustrate these ideas, we focus on lattice models with SO (N ) symmetric interactions, and study the phase transition between the trivial and the topological gapless phases using bosonization and a weak-coupling renormalization group analysis. As a concrete example, we study in detail the case of N = 3. We show that in this case, the topologically non-trivial superconducting phase corresponds to a gapless analogue of the Haldane phase in spin-1 chains. In this phase, although the bulk is gapless to single particle excitations, the ends host spin-1/2 degrees of freedom which are exponentially localized and protected by the spin gap in the bulk. We obtain the full phase diagram of the model numerically, using density matrix renormalization group calculations. Within this model, we identify the self-dual line studied by Andrei and Destri [Nucl. Phys. B, 231(3), 445-480 (1984)], as a first-order transition line between the gapless Haldane phase and a trivial gapless phase. This allows us to identify the propagating spin-1/2 kinks in the Andrei-Destri model as the topological end-modes present at the domain walls between the two phases.

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“…where K is the Luttinger parameter. As the Θ field in (15) is conjugate to the total density of particles, n(x) = N a=1 n a (x),…”

Section: Low-energy Description Of the Topological Phasementioning

confidence: 99%

“…As we show below, this is a consequence of both the presence of a flavor gap and of the topological nature of the phase. The gapless excitations of the generalized Luttinger liquid (15) can be expressed in terms of the vertex operators…”

Section: Low-energy Description Of the Topological Phasementioning

confidence: 99%

From one-dimensional charge conserving superconductors to the gapless Haldane phase

2018

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“…The second direction exploits the emergent helical protected states in interacting systems which are not necessarily time-reversal invariant. Numerous examples of suitable interactions include the hyperfine interaction between nuclei moments and conduction electrons [16][17][18][19][20], the spin-orbit interaction in combination with either a magnetic field [21,22] or with the Coulomb interaction [23,24], to name just a few; see references [25][26][27][28][29][30]. State-of-the-art experiments confirm the existence of helical states governed by interactions [31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Transport in magnetically doped one-dimensional wires: can the helical protection emerge without the global helicity?

Tsvelik

Yevtushenko

2020

New J. Phys.

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We study the phase diagram and transport properties of arbitrarily doped quantum wires functionalized by magnetic adatoms. The appropriate theoretical model for these systems is a dense one-dimensional Kondo lattice (KL) which consists of itinerant electrons interacting with localized quantum magnetic moments. We discover the novel phase of the locally helical metal where transport is protected from a destructive influence of material imperfections. Paradoxically, such a protection emerges without a need of the global helicity, which is inherent in all previously studied helical systems and requires breaking the spin-rotation symmetry. We explain the physics of this protection of the new type, find conditions, under which it emerges, and discuss possible experimental tests. Our results pave the way to the straightforward realization of the protected ballistic transport in quantum wires made of various materials. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft New J. Phys. 22 (2020) 053013 A M Tsvelik and O M Yevtushenkohelix spin configuration which gaps out one helical sector of the electrons. The second helical sector remains gapless. In the resulting helical metal (HM), the disorder induced localization is parametrically suppressed and, therefore, the ballistic transport acquires a partial protection [66,67].All previous studies, including the TIs and the interacting helical systems, revealed protection of transport governed by the global helicity, i.e., helicity of the gapless electrons and/or the spiral spin configuration were uniquely defined in the entire sample. The global helicity always requires breaking the spin-rotation symmetry, either internally (e.g., due to the spin-orbit interaction, or the magnetic anisotropy) or spontaneously (e.g. in relatively short samples with a strong electrostatic interaction of the electrons). This certainly diminishes experimental capabilities to fabricate the helical states, especially those governed by the interactions: one always needs either specially selected materials or a nontrivial fine-tuning of physical parameters. For instance, the prediction of references [66,67] remains practically useless for the experiments because one can hardly control the magnetic anisotropy.Thus, further progress in obtaining the helical quantum wires, in particular by means of the magnetic doping, has been hampered by two open questions: (i) is the global helicity accompanied by breaking the spin-rotation symmetry really necessary to obtain HM? (ii) If the global helicity is not really needed, which parameters must be tuned for detecting HM in the KLs (theoretically) and in the magnetically doped quantum wires (experimentally)? We note that numerical studies have never provided a reliable signature of the helical phase in the KLs [53,61,65].In this paper, we answer both questions: protection of the ballistic transport can be provided by the local helicity which, paradoxically, requires neither the glo...

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“…Generically, in a non-interacting system, these modes can hybridise and be localised by the presence of sufficient density of impurities, making the system topologically trivial. Surprisingly, in the presence of interaction, there is some possibility for these modes to be protected against localisation, by a zero bias anomaly mechanism in the case of vanishing tunneling [23] or by the emergence of an effective spin gap [24,25] that suppresses single particle backscattering when tunneling is arXiv:1805.10045v2 [cond-mat.str-el] 23 Oct 2018 present. In these cases, the system displays topological signatures like a robust value of conductance, quantized in units of e 2 /h and fractionalised zero modes in domain wall configurations.…”

Section: Introductionmentioning

confidence: 99%

Interplay between intrinsic and emergent topological protection on interacting helical modes

2019

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The interplay between topology and interactions on the edge of a two dimensional topological insulator with time reversal symmetry is studied. We consider a simple non-interacting system of three helical channels with an inherent Z2 topological protection, and hence a zero-temperature conductance of G = e 2 /h. We show that when interactions are added to the model, the ground state exhibits two different phases as function of the interaction parameters. One of these phases is a trivial insulator at zero temperature, as the symmetry protecting the non-interacting topological phase is spontaneously broken. In this phase there is zero conductance (G = 0) at zerotemperature. The other phase displays enhanced topological properties, with a topologically protected zero-temperature conductance of G = 3e 2 /h and an emergent Z3 symmetry not present in the lattice model. The neutral sector in this phase is described by a massive version of Z3 parafermions. This state is an example of a dynamically enhanced symmetry protected topological state.

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Interaction induced topological protection in one‐dimensional conductors

Cited by 23 publications

References 31 publications

From one-dimensional charge conserving superconductors to the gapless Haldane phase

From one-dimensional charge conserving superconductors to the gapless Haldane phase

Transport in magnetically doped one-dimensional wires: can the helical protection emerge without the global helicity?

Interplay between intrinsic and emergent topological protection on interacting helical modes

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