Helical edge transport in the presence of a magnetic impurity: The role of local anisotropy

Kurilovich, Vladislav D.; Kurilovich, Pavel D.; Burmistrov, I. S.; Goldstein, Moshe

doi:10.1103/physrevb.99.085407

Cited by 24 publications

(27 citation statements)

References 65 publications

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“…We note that when considering the case of an impurity spin with spin larger than 1/2, the Hamiltonian may also include spin-anisotropy terms M α (S α ) 2 which are nontrivial. These terms may play an important role in driving backscattering current in such setups [45,47].…”

Section: Interaction Hamiltonian and Perturbative Rg Analysismentioning

confidence: 99%

“…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: Interaction Hamiltonian and Perturbative Rg Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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“…Recently, a practical way of inducing QSH states has been suggested also for graphene, by exploiting heavy ad-atom deposition [73][74][75]. While previous works [76][77][78][79][80][81][82] analyzed ordinary shot noise due to magnetic impurities on the QSH edge, investigations of delta-T noise in this system has so far been lacking.…”

Section: B Overview Of Models and Resultsmentioning

confidence: 99%

Does delta-$T$ noise probe quantum statistics?

Z¹,

Gornyi²,

Spånslätt³

2022

Preprint

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We study delta-T noise-excess charge noise at zero voltage but finite temperature bias-for weak tunneling in one-dimensional interacting systems. We show that the sign of the delta-T noise is generically determined by the nature of the dominating tunneling process. More specifically, the sign is governed by the leading charge-tunneling operator's scaling dimension. We clarify the relation between the sign of delta-T noise and the quantum exchange statistics of tunneling quasiparticles. We find that, for infinite systems hosting chiral channels with local interactions (e.g., quantum Hall or quantum spin Hall edges), when the delta-T noise is negative, the tunneling particles are boson-like, revealing their tendency towards bunching. However, the opposite is not true: Bosonlike particles do not necessarily produce negative delta-T noise. Importantly, the bosonic nature of particles generating the negative delta-T is not necessarily intrinsic, but can be induced by the interactions. This, in particular, implies that negative delta-T noise for tunneling between the edge states cannot serve as a smoking gun for detecting "intrinsic anyons". We also establish a connection between the delta-T noise and the temperature derivative of the Nyquist-Johnson (thermal) noise in interacting systems, both governed by the same scaling dimensions. As a demonstration of the above statements, we study tunneling between two interacting quantum spin Hall edges. With bosonization and renormalization-group techniques, we find that many-body interactions can generate negative delta-T noise for both direct tunneling through a point contact and in Kondo exchange tunneling via a localized spin. In both these setups, we show that the noise can become negative at sufficiently low temperatures, when interactions renormalize the tunneling to favor boson-like pair-tunneling of electrons rather than single-electron tunneling. Our findings show that delta-T noise can be used to probe the nature of collective excitations in interacting one-dimensional systems.

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“…The latter violation is required to generate persistent backscattering of helical electrons. We assume that the coupling constants are small, |J ij | 1, and we neglect the local anisotropy H anis = D kp S k S p of the MI spin which is justified at |D kp | max{J 2 ij T, |J ij |V } [47]. In the absence of the local anisotropy we can rotate the spin basis for S i bringing the exchange matrix J ij to a lower triangular form.…”

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confidence: 99%

Unrestricted Electron Bunching at the Helical Edge

Kurilovich

Burmistrov

et al. 2019

Phys. Rev. Lett.

Self Cite

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A quantum magnetic impurity of spin S at the edge of a two-dimensional time reversal invariant topological insulator may give rise to backscattering. We study here the shot noise associated with the backscattering current for arbitrary S. Our full analytical solution reveals that for S > 1 2 the Fano factor may be arbitrarily large, reflecting bunching of large batches of electrons. By contrast, we rigorously prove that for S = 1 2 the Fano factor is bounded between 1 and 2, generalizing earlier studies.

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Helical edge transport in the presence of a magnetic impurity: The role of local anisotropy

Cited by 24 publications

References 65 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

Does delta-$T$ noise probe quantum statistics?

Unrestricted Electron Bunching at the Helical Edge

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