Magnetic moments in a helical edge can make weak correlations seem strong

Väyrynen, Jukka I.; Geißler, Florian; Glazman, L. I.

doi:10.1103/physrevb.93.241301

Cited by 53 publications

(57 citation statements)

References 35 publications

(67 reference statements)

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“…The question of the effect of magnetic impurities on the conductance along helical edges was the subject of theoretical attention as well, considering different forms of impurities, coupling, and electronic band structures [35][36][37][38][39][40][41][42][43][44][45][46][47]. At low temperatures and in the absence of strong electron-electron interactions, a generic magnetic impurity forms a Kondo singlet and is screened out, allowing the helical edge to reconstitute itself around it and, therefore, has no effect on the conductance.…”

Section: Introductionmentioning

confidence: 99%

“…They showed that this can be understood due to the fact that timereversal symmetry allows backscattering only accompanied with a spin-flip of the impurity, which can be further flipped back only with backscattering in the opposite direction, thus prohibiting a steady-state backscattered current. In order to circumvent this limitation while preserving time-reversal symmetry, one has to consider an anisotropic exchange coupling [38,[45][46][47] or describe coupling to a many-level interacting quantum dot [29,40,43].…”

Section: Introductionmentioning

confidence: 99%

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Analytical and numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity

2020

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We study the conductance of a time-reversal symmetric helical electronic edge coupled antiferromagnetically to a magnetic impurity, employing analytical and numerical approaches. The impurity can reduce the perfect conductance G0 of a noninteracting helical edge by generating a backscattered current. The backscattered steady-state current tends to vanish below the Kondo temperature TK for time-reversal symmetric setups. We show that the central role in maintaining the perfect conductance is played by a global U (1) symmetry. This symmetry can be broken by an anisotropic exchange coupling of the helical modes to the local impurity. Such anisotropy, in general, dynamically vanishes during the renormalization group (RG) flow to the strong coupling limit at low-temperatures. The role of the anisotropic exchange coupling is further studied using the time-dependent Numerical Renormalization Group (TD-NRG) method, uniquely suitable for calculating out-of-equilibrium observables of strongly correlated setups. We investigate the role of finite bias voltage and temperature in cutting the RG flow before the isotropic strong-coupling fixed point is reached, extract the relevant energy scales and the manner in which the crossover from the weakly interacting regime to the strong-coupling backscattering-free screened regime is manifested. Most notably, we find that at low temperatures the linear conductance of the backscattering current follows a power-law behavior G ∼ (T /TK ) 2 , and the strong exponent implies that the anisotopry might be a dominant cause for reducing the perfect edge conductance. arXiv:1912.02838v1 [cond-mat.str-el] 5 Dec 2019 Q S H I Impurity site t J I B e/(G 0 Γ) (b) J yy /Γ =1 J yy /Γ =0.7 J yy /Γ =0.5 J yy /Γ =0.3 J yy /Γ =0.1 0.0 0.2 0.4 0.6 0.8 1.0 J yy /Γ T eq K eG/(G 0 Γ) ·10 3(a) J yy /Γ =0.9 J yy /Γ =0.7 J yy /Γ =0.5 J yy /Γ =0.3 J yy /Γ =0.1

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical and numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity

2020

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“…Furthermore, even in the absence of time-reversal symmetry breaking, electronelectron interactions may induce backscattering [18], resulting in the suppression of the helical edge conductance at finite temperatures (see [19] and references therein). A combination of electron-electron interactions and magnetic impurities can significantly modify the picture of ideal helical edge transport [20][21][22][23][24].…”

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Helical edge transport in the presence of a magnetic impurity

Kurilovich

Burmistrov

et al. 2017

Jetp Lett.

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We consider the effects of electron scattering off a quantum magnetic impurity on the current-voltage characteristics of the helical edge of a two-dimensional topological insulator. We compute the backscattering contribution to the current along the edge for a general form of the exchange interaction matrix and arbitrary value of the magnetic impurity spin. We find that the differential conductance may exhibit a non-monotonous dependence on the voltage with several extrema. PACS:Introduction. -Two-dimensional topological insulators (2D TIs) are in the focus of recent interest due to existence of two helical edge states inside the band gap [1,2]. Because of spin-momentum locking caused by strong spin-orbit coupling, electrical current transfers helicity along the edge [3,4]. This "spin" current is a hallmark of the quantum spin Hall effect, and it has been detected experimentally in HgTe/CdTe quantum wells [5][6][7][8][9]. If only elastic scattering is allowed, and in the absence of time-reversal symmetry breaking, the helical state is a realization of the ideal transport channel with conductance of G 0 = e 2 /h. This prediction was questioned by the experiments in HgTe/CdTe [5,[10][11][12] and InAs/GaSb [13,14] quantum wells. Therefore, studies of mechanisms which can lead to the destruction of the ideal helical transport are important.A local perturbation breaking the time-reversal symmetry, e.g., a classical magnetic impurity, leads to backscattering of helical edge states and reduction of the edge conductance [15,16]. Electron-electron interactions along the edge can promote edge reconstruction and, consequently, spontaneous time-reversal symmetry breaking at the edge [17]. Furthermore, even in the absence of time-reversal symmetry breaking, electronelectron interactions may induce backscattering [18], resulting in the suppression of the helical edge conductance at finite temperatures (see [19] and references therein). A combination of electron-electron interactions and magnetic impurities can significantly modify the picture of ideal helical edge transport [20][21][22][23][24].In the absence of electron-electron interactions along the edge, the ideal transport along the helical edge may

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“…One dimensional (1D) helical edge modes of two-dimensional TIs possess lock-in relation between electron spin and momentum [4,5]. Though this locking may protect transport against disorder [6][7][8], the protection in realistic TIs is not perfectly robust; reasons for this remain an open and intensively debated question [6][7][8][9][10][11][12][13][14][15].…”

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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Magnetic moments in a helical edge can make weak correlations seem strong

Cited by 53 publications

References 35 publications

Analytical and numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity

Analytical and numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity

Helical edge transport in the presence of a magnetic impurity

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

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