Controlling spin polarization of a quantum dot via a helical edge state

Abstract

We investigate a Zeeman-split quantum dot (QD) containing a single spin 1/2 weakly coupled to a helical Luttinger liquid (HLL) within a generalized master equation approach. The HLL induces a tunable magnetization direction on the QD controlled by an applied bias voltage when the quantization axes of the QD and the HLL are noncollinear. The backscattering conductance (BSC) in the HLL is finite and shows a resonance feature when the bias voltage equals the Zeeman energy in magnitude. The observed BSC asymmetry in bias voltage directly reflects the quantization axis of the HLL spin.PACS numbers: 73.23. Hk, 72.10.Fk, 71.10.Pm The hallmark of time reversal invariant topological insulators (TI) [1,2] in two dimensions is the quantum spin Hall (QSH) effect. The edge states forming at the boundary of the QSH device are counterpropagating Kramers pairs. The QSH effect was proposed and measured in HgTe/CdTe [3][4][5] and InAs/GaSb quantum wells (QWs) [6,7]. The spin polarization in the edge state transport has been demonstrated by combining the QSH effect and the spin Hall effect [8]. The QSH edge states form a helical Luttinger liquid (HLL) [9] in the presence of electronelectron interactions.The helical structure imposes strong restrictions for backscattering, and allows many mechanisms to be potentially important. Effects of single spin impurities coupled to a HLL for isotropic [10][11][12][13] and anisotropic Kondo models [13][14][15], as well as in tight-binding models for graphene ribbons with spin orbit interaction within the Kane-Mele model [16][17][18][19] have been considered. In a similar context, the effect of backscattering by nuclear background spins [20] and the implications of this background for Rashba scattering [21] have also been studied. In all these works, no dc backscattering current is found without intrinsic spin relaxation, an anisotropic Kondo coupling or Rashba impurity, due to the necessity to flip the spin in order to scatter between opposite branches of the QSH edge. This characteristic is reminiscent of QDs coupled to bulk (3D) ferromagnetic leads, where the coupling to the leads controls the QD behavior, and virtual exchange of electrons induces an exchange field on the QD parallel to the lead polarization [22][23][24] adding to possible external fields [25,26].In this work, we discuss a setup in which a QD in the cotunneling regime is coupled to the QSH device, which acts as a spin polarized reservoir. In order to manipulate the spin on the QD, we assume that a magnetic field is applied to the QD, inducing a quantization axis that is not parallel with that of the QSH states that is determined by spin-orbit interaction. The resulting dynamics Figure 1. Setup considered in this paper (a) and construction of the effective QD Hamiltonian (b). A HLL is coupled to a QD described by a Kondo Hamiltonian HK . A magnetic field B is applied to the QD, which is tilted with respect to the quantization axisẑ of the helical edge state (fixed by the helical edge) by an angle θZ . The effective system...

Optimal Thermoelectricity with Quantum Spin Hall Edge States

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Transport in quantum spin Hall edges in contact to a quantum dot

“…The coupling of helical edge states to quantum dots and magnetic impurities has been addressed in several works. [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] A crucial ingredient for a net resistive…”

Helical spin thermoelectrics controlled by a side-coupled magnetic quantum dot in the quantum spin Hall state

“…[46][47][48][49][50] Charge transport in helical edges of the quantum spin Hall regime with tunneling contacts between edge states and quantum dots or antidots is a subject of very active theoretical investigation. [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67] arXiv:1808.05570v2 [cond-mat.str-el] 20 Nov 2018…”