Spin-pumping and inelastic electron tunneling spectroscopy in topological insulators

Aaron Hurley, Awadhesh Narayan, and Stefano Sanvito

Phys. Rev. B 87, 245410 – Published 6 June 2013

Abstract

We demonstrate that a quantum spin Hall current, spontaneously generated at the edge of a two-dimensional topological insulator, acts as a source of spin pumping for a magnetic impurity with uniaxial anisotropy. One can then manipulate the impurity spin direction by means of an electrical current without using either magnetic electrodes or an external magnetic field. Furthermore we show that the unique properties of the quantum spin Hall topological state have profound effects on the inelastic electron tunneling spectrum of the impurity. For low current densities inelastic spin-flip events do not contribute to the conductance. As a consequence the conductance steps, normally appearing at voltages corresponding to the spin excitations, are completely suppressed. In contrast an intense current leads to spin pumping and generates a transverse component of the impurity spin. This breaks the topological phase yielding to the conductance steps.

Received 7 September 2012

DOI:https://doi.org/10.1103/PhysRevB.87.245410

Authors & Affiliations

Aaron Hurley, Awadhesh Narayan, and Stefano Sanvito

School of Physics and CRANN, Trinity College, Dublin 2, Ireland

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Issue

Vol. 87, Iss. 24 — 15 June 2013

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Images

Figure 1
Schematic representation of the device considered in this work (a), comprising a TI with honeycomb lattice structure and a magnetic impurity adsorbed at one of the two edges. In the transport calculations the electronic structures of the electrodes are described by the self-energies, $Σ_{η}$ ( $η = L, R$ ). In panel (b) the cartoons describe a spin-flip scattering event. A right-going electron with up-spin direction (left panel) is inelastically backscattered by the magnetic impurity. In the process both the electron and the impurity spins are reversed (right panel). Note that, given the topological nature of the ribbon, spin flip forbids electron transmission as the edge presenting a right-going spin-up state does not possess a right-going spin-down one.Reuse & Permissions
Figure 2
Spin-polarized IETS conductance spectrum for a TI (11,6) ribbon with an $S = 1$ magnetic impurity attached at the upper edge. Note that the conductance step at the voltage characteristic of the inelastic excitation gets suppressed as the $t_{2}$ parameter is increased, i.e., as the ribbon is brought well inside the topological region of the phase diagram.Reuse & Permissions
Figure 3
(a) Nonequilibrium population as a function of bias of the $S = 1$ impurity spin states for a (7,4) (broken lines) and an (11,6) ribbon (solid lines). In panel (b) we show the average magnetization of the impurity for the same ribbons.Reuse & Permissions
Figure 4
Spin-polarized IETS conductance spectrum for a TI (11,6) ribbon with an $S = 1$ magnetic impurity attached at the upper edge. In this case the current is intense and drives the impurity spin away from the uniaxial anisotropy axis (see Fig. 3). Notably now there is a step in the differential conductance at the voltage corresponding to the inelastic transition $| \pm 1 〉 \to | 0 〉$ . The magnitude and sign of such step depends on the bias polarity. The inset shows the inelastic contribution to the conductance.Reuse & Permissions
Figure 5
Spin-polarized IETS conductance spectrum for a TI (11,6) ribbon incorporating a magnetic impurity with various spin ( $S = 1, 3 / 2, 2, 3$ ) attached at the upper edge, in the intense current regime. The step in the differential conductance increases in magnitude with increasing the spin value of the adatom. Note that the spectra have been aligned vertically for clarity of comparison. The inset shows the average magnetization of the impurity for different values of $S$ . Note that spin pumping persists for the larger values of the impurity spin.Reuse & Permissions

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