Indirect exchange interaction between magnetic impurities in the two-dimensional topological insulator based on CdTe/HgTe/CdTe quantum wells

et al. 2019

Phys. Rev. B

Helical edge modes of 2D topological insulators are supposed to be protected from time-reversal invariant elastic backscattering. Yet substantial deviations from the perfect conductance are typically observed experimentally down to very low temperatures. To resolve this conundrum we consider the effect of a single magnetic impurity with arbitrary spin on the helical edge transport. We consider the most general structure of the exchange interaction between the impurity and the edge electrons. We take into the account the local anisotropy for the impurity and show that it strongly affects the backscattering current in a wide range of voltages and temperatures. We show that the sensitivity of the backscattering current to the presence of the local anisotropy is different for half-integer and integer values of the impurity spin. In the latter case the anisotropy can significantly increase the backscattering correction to the current. arXiv:1808.03084v2 [cond-mat.mes-hall]

Section: Modelmentioning

confidence: 99%

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

et al. 2019

Phys. Rev. B

“…The presence of inversion asymmetry of the CdTe/HgTe/CdTe quantum well [33][34][35][36] results in even more complicated spin structure of the IEI, which becomes non-invariant under rotations in the plane of the QW. Besides, oscillations of the IEI with the distance appear [24].…”

Section: Introductionmentioning

confidence: 97%

“…In this case the IEI has rather complicated spin structure and decays exponentially with the distance at low temperatures provided that the chemical potential is pinned to the gap. It involves anisotropic XXZ Heisenberg interaction, magnetic pseudodipole interaction, and Dzyaloshinsky-Moriya interaction [24]. Such spin structure is typical for systems with a strong spin-orbit coupling, e.g.…”

Section: Introductionmentioning

confidence: 99%

Indirect exchange interaction between magnetic impurities near the helical edge

2017

Phys. Rev. B

Self Cite

The indirect exchange interaction between magnetic impurities located in the bulk of a twodimensional topological insulator decays exponentially with the distance. The indirect exchange interaction for magnetic impurities mediated by the helical states at the edge of the topological insulator demonstrates behaviour which is typical for the Ruderman-Kittel-Kasuya-Yosida interaction in a one-dimensional metal. We have shown that interference between the bulk and edge states in the two-dimensional topological insulator results in existence of the unusual contribution to the indirect exchange interaction which, on the one hand, decays exponentially with a distance at the length scale controlled by the Fermi energy of the edge states and, on the other hand, oscillates with distance along the helical edge with the period determined by the Fermi wave length. We found that this interference contribution to the indirect exchange interaction becomes dominant for such configurations of two magnetic impurities when one of them is situated close to the helical edge whereas the other one is located far away in the bulk.

“…For a (001) CdTe/HgTe/CdTe QW with width close to the critical one, 6.3 nm, the exchange couplings |J m |, |J z |, |J 0 | for a Mn impurity can be estimated to be of the order of 0.1 eV · nm 2 [30]. Using the estimates ν 0.5 eV −1 · nm −1 and ξ 40 nm [1], we find that the exchange couplings J jk are of the order 10 −3 .…”

mentioning

confidence: 99%

“…After the projection onto the subspace of 2D electron and hole states |E 1 , + , |H 1 , + , |E 1 , − , |H 1 , − , the Hamiltonian of a magnetic impurity with spin S situated at some point {x 0 , y 0 , z 0 } within the (001) quantum well can be written as follows [28,30]:…”

mentioning

confidence: 99%

Helical edge transport in the presence of a magnetic impurity

et al. 2017

Jetp Lett.

Self Cite

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