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Register a new userNon-local control of spin-spin correlation in finite geometry helical edge
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An infinite edge of a quantum Hall system prohibits indirect exchange coupling between two spins whereas a quantum spin-Hall edge prohibits out-of-plane coupling. In this study we analyze an unexpected breakdown of this behaviors in a finite system, where the two spins can interact also via a longer path that traverses the whole perimeter of the system. We explain this using an analytical model as well as using tight binding models in real space. Based on this finding, we propose how using a lead far away from the spins can switch the coupling on and off among them non-locally.
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We calculate the frequency-dependent shot noise in the edge states of a two-dimensional topological insulator coupled to a magnetic impurity with spin $S=1/2$ of arbitrary anisotropy. If the anisotropy is absent, the noise is purely thermal at low frequencies, but tends to the Poissonian noise of the full current $I$ at high frequencies. If the interaction only flips the impurity spin but conserves those of electrons, the noise at high voltages $eVgg T$ is frequency-independent. Both the noise and the backscattering current $I_{bs}$ saturate at voltage-independent values. Finally, if the Hamiltonian contains all types of non-spin-conserving scattering, the noise at high voltages becomes frequency-dependent again. At low frequencies, its ratio to $2eI_{bs}$ is larger than 1 and may reach 2 in the limit $I_{bs}to 0$. At high frequencies it tends to 1.
This is the reply to the comment by I. S. Burmistrov, P. D. Kurilovich, and V. D. Kurilovich [arXiv:1903.047241] on our paper Noise in the helical edge channel anisotropically coupled to a local spin [JETP Lett. 108, 664 (2018), arXiv:1810.05831].
The presence of edges locally breaks the inversion symmetry of heterostructures and gives rise to lateral (edge) spin-orbit coupling (SOC), which, under some conditions, can lead to the formation of helical edge states. If the edge SOC is strong enough, the helical edge states can penetrate the band-gap and be energetically isolated from the bulk-like states. As a result backward scattering is suppressed, dissipationless helical edge channels protected against time-inversion symmetric perturbations emerge, and the system behaves as a 2D topological insulator (TI). However, unlike in previous works on TIs, the mechanism proposed here for the creation of protected helical edge states relies on the strong edge SOC rather than on band inversion.
It is widely admitted that the helical conformation of certain chiral molecules may induce a sizable spin selectivity observed in experiments. Spin selectivity arises as a result of the interplay between a helicity-induced spin-orbit coupling and electric dipole fields in the molecule. From the theoretical point of view, different phenomena might affect the spin dynamics in helical molecules, such as quantum dephasing, dissipation and the role of metallic contacts. Previous studies neglected the local deformation of the molecule about the carrier thus far, but this assumption seems unrealistic to describe charge transport in molecular systems. We introduce an effective model describing the electron spin dynamics in a deformable helical molecule with weak spin-orbit coupling. We find that the electron-lattice interaction allows the formation of stable solitons such as bright solitons with well defined spin projection onto the molecule axis. We present a thorough study of these bright solitons and analyze their possible impact on the spin dynamics in deformable helical molecules.
Magnetic impurities with sufficient anisotropy could account for the observed strong deviation of the edge conductance of 2D topological insulators from the anticipated quantized value. In this work we consider such a helical edge coupled to dilute impurities with an arbitrary spin $S$ and a general form of the exchange matrix. We calculate the backscattering current noise at finite frequencies as a function of the temperature and applied voltage bias. We find that in addition to the Lorentzian resonance at zero frequency, the backscattering current noise features Fano-type resonances at non-zero frequencies. The widths of the resonances are controlled by the spectrum of corresponding Korringa rates. At a fixed frequency the backscattering current noise has non-monotonic behaviour as a function of the bias voltage.
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