Kondo lattice on the edge of a two-dimensional topological insulator

Maciejko, Joseph

doi:10.1103/physrevb.85.245108

Cited by 50 publications

(80 citation statements)

References 63 publications

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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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confidence: 99%

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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confidence: 99%

Helical edge transport in the presence of a magnetic impurity

Kurilovich

Burmistrov

et al. 2017

Jetp Lett.

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“…6 the global phase diagram in the plane spanned by λ F and g for fixed λ B = 0.1. As pointed out in the previous studies [21], there are two phases: the screened phase (SC) where the Kondo effect leads to a screening of the impurity and the local moment (LM) phase where spinflips are completely suppressed for T → 0. The phase boundary for λ B = 0.1 is well described by the recent renormalization group results for λ B ≪ λ F represented by the dashed line [21].…”

Section: Phase Diagrammentioning

confidence: 88%

“…In this subsection, we examine the spin-1/2 XXZ Kondo model [19][20][21]. We restrict our analysis to the case where the total spin in the z direction is conserved.…”

Section: B Xxz Kondo Model In Helical Liquidsmentioning

confidence: 99%

“…The main results in this subsection are the phase diagram in g-λ B plane, which has been discussed perturbatively [19,21] and the numerically-exact time and temperature dependence of the spin-spin correlation functions for general interaction parameters.…”

Section: B Xxz Kondo Model In Helical Liquidsmentioning

confidence: 99%

“…This enables ones to implement the CTQMC for the TLL easily from their fermionic CTQMC code. (iv) The method can be applicable to not only potential scattering problems but also to Kondo-type problems [19][20][21] without a negative sign problem. (v) The electron Green's functions, the boson-boson correlations, conductance, the spin-spin correlation functions, and various local correlators are calculable.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum impurity in a Tomonaga-Luttinger liquid: Continuous-time quantum Monte Carlo approach

Hattori

Rosch

2014

Phys. Rev. B

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We develop a continuous-time quantum Monte Carlo (CTQMC) method for quantum impurities coupled to interacting quantum wires described by a Tomonaga-Luttinger liquid. The method is negative-sign free for any values of the Tomonaga-Luttinger parameter, which is rigorously proved, and thus, efficient low-temperature calculations are possible. Duality between electrons and bosons in one dimensional systems allows us to construct a simple formula for the CTQMC algorithm in these systems. We show that the CTQMC for Tomonaga-Luttinger liquids can be implemented with only minor modifications of previous CTQMC codes developed for impurities coupled to noninteracting fermions. We apply this method to the Kane-Fisher model of a potential scatterer in a spin-less quantum wire and to a single spin coupled with the edge state of a two-dimensional topological insulator assuming an anisotropic XXZ coupling. Various dynamical response functions such as the electron Green's function and spin-spin correlation functions are calculated numerically and their scaling properties are discussed.

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Natural orbitals renormalization group approach to a Kondo singlet

Zheng

2020

Sci. China Phys. Mech. Astron.

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Using the natural orbitals renormalization group, we studied the problem of a localized spin-1 2 impurity coupled to two helical liquids via the Kondo interaction in a quantum spin Hall insulator, based on the Kane-Mele model defined in a finite zigzag graphene nanoribbon. We investigated the influence of the Kondo couplings with the helical liquids on both the static and dynamic properties of the ground state. The number and distinct spatial structures of the active natural orbitals (ANOs), which play essential roles in constructing the ground-state wave function, were first analyzed. Our numerical results indicate that two ANOs emerge, equal to the number of helical liquids. Specifically, at the coupling symmetry point, both ANOs are fully active with their spatial structures being respectively constituted by the different helical liquids. In comparison, when deviating from the symmetry point, only one ANO remains fully active, which is dominantly constructed by the helical liquid with the larger Kondo coupling. Local screening of the impurity, described by the impurity spin polarization and susceptibility, was further studied. It shows that at the coupling symmetry point, the impurity is maximally polarized and the spin susceptibility reaches the maximum. On the contrary, the impurity tends to be screened without polarization when the Kondo couplings deviate well from the symmetry point. The Kondo screening cloud, manifested by the spin correlation between the impurity and the conduction electrons, was finally explored. It is demonstrated that the Kondo cloud is mainly formed by the helical liquid with the larger Kondo coupling to the impurity. On the other hand, the spin-orbital coupling breaks the symmetry in spatial distribution of the spin correlation, leading to anisotropy in the Kondo cloud.

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Kondo lattice on the edge of a two-dimensional topological insulator

Cited by 50 publications

References 63 publications

Helical edge transport in the presence of a magnetic impurity

Helical edge transport in the presence of a magnetic impurity

Quantum impurity in a Tomonaga-Luttinger liquid: Continuous-time quantum Monte Carlo approach

Natural orbitals renormalization group approach to a Kondo singlet

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