Pauli spin blockade with site-dependent $g$ tensors and spin-polarized leads

Philipp M. Mutter and Guido Burkard

Phys. Rev. B 103, 245412 – Published 10 June 2021

Abstract

Pauli spin blockade in double quantum dots has matured into a prime technique for precise measurements of nanoscale system parameters. In this work we demonstrate that systems with site-dependent $g$ tensors and spin-polarized leads allow for a complete characterization of the $g$ tensors in the dots by magnetotransport experiments alone. Additionally, we show that special polarization configurations can enhance the often elusive magnetotransport signal, rendering the proposed technique robust against noise in the system and inducing a giant tunnel magnetoresistance effect. Finally, we incorporate the effects of the spin-orbit interaction and show that in this case the leakage current contains information about the $g$ tensors and the degree of spin polarization in the leads.

Received 9 March 2021
Revised 21 May 2021
Accepted 25 May 2021

DOI:https://doi.org/10.1103/PhysRevB.103.245412

Physics Subject Headings (PhySH)

Magnetotransport Spin blockade Spin-orbit coupling

Quantum dots Semiconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Philipp M. Mutter ^* and Guido Burkard^†

Department of Physics, University of Konstanz, D-78457 Konstanz, Germany

^*philipp.mutter@uni-konstanz.de
^†Corresponding author: guido.burkard@uni-konstanz.de

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Issue

Vol. 103, Iss. 24 — 15 June 2021

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Images

Figure 1
Basic setup for PSB with completely polarized leads. When a bias voltage is applied, electrons may tunnel from the left lead to the left dot with rate $Γ^{'}$ and from the right dot to the right lead with rate $Γ$ (blue arrows), thereby creating a charge cycle. Once in the DQD, the states in the (1,1) charge configuration must transition to the singlet in the (0,2) charge configuration aided by the interdot tunnel coupling $t$ (green arrow). A characteristic feature of completely polarized leads is that one spin making up this singlet is unable to leave the system (solid black arrows). (a) One case of complete and parallel polarizations in the leads, $p_{L} p_{R} = 1$ , and (b) one case of complete and antiparallel polarizations, $p_{L} p_{R} = - 1$ .
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Figure 2
Visualization of the effective rate approach. In the full five-state model, the unpolarized triplet state $| T_{0} 〉$ transitions with a rate $Γ_{rel}$ to another state (to any particular of the three remaining states with a rate $Γ_{rel} / 3$ ). Blue arrows indicate transitions within the triplet subspace, while red arrows indicate one-way transitions from the triplets to the singlet in the (1,1) configuration, which will subsequently tunnel into the (0,2) configuration without further relaxation. In the three-state model one may combine all these rates into a single effective rate $Γ_{TS}$ from the unpolarized triplet to the singlet [purple arrow, Eq. (7)].
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Figure 3
Leakage current for $p_{L} p_{R} = 1$ . (a) The exact analytical magnetotransport curve $I_{0} (B_{k})$ as given by Eq. (9). It shows a distinct maximum at $B_{k}^{*} = \sqrt{2} t / g_{k}^{-}$ independent of the detuning $Δ$ . (b) The leakage current, including high-temperature relaxation processes at zero detuning, $Δ = 0$ . We find good agreement between the numerical data points and the analytical result (gray line). In particular, the zero-field value is finite and agrees well with the analytical result, Eq. (10). For the sake of clarity, the curves and numerical data points are shifted by constant values as indicated in the figure. The dot-lead tunneling rate was set to $Γ = 0.1 t$ for both plots.
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Figure 4
Leakage current $I (p_{L}, p_{R})$ as a function of the DSPs in the left and right leads. (a) The case of a vanishing field along $z$ , and (b) the case of the magnetic field fixed at the $g$ -tensor resonance of the system, $B_{z}^{*} = t / \sqrt{g_{z}^{L} g_{z}^{R}}$ . The regions in the $p_{L} − p_{R}$ plane for which the current is highest are exchanged as the magnetic field is increased, an observation that can be explained on grounds of energy considerations (see text). The blue circles indicate the points used in calculating a giant tunnel magnetoresistance via Eq. (12). (c) The normalized ratio of the rate of the polarized triplet $| T_{-} 〉$ transitioning to the (0,2) configuration, $Γ_{-}$ , and the rate of the hybridized states $| α_{0, \pm} 〉$ transitioning to the (0,2) configuration, $Γ_{α}$ , as a function of the magnetic field. The parameter values used for all plots are $Δ = 0$ , $g_{z}^{L} = 5.5$ , $g_{z}^{R} = 5.4$ , $g_{x}^{L} = 0.4$ , $g_{x}^{R} = 0.3$ , $Γ_{rel} = 0.001 t$ , $Γ_{R} = 0.01 t$ , and $B_{x} = 0.1 t$ .
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Figure 5
Leakage current in the presence of spin-flip tunneling processes induced by the SOI. We plot the current $I$ as a function of the detuning $Δ$ and compare the numerical results (dots) to the analytical expressions [solid lines, Eq. (16)]. The current is enhanced for nonzero lead polarizations if $p_{L} p_{R} > 0$ (orange curve). When the DSPs differ in the two leads, the current becomes asymmetric in the detuning (blue curve). We set $B_{z} = 0.3 t$ , $g_{z}^{L} = 5.5$ , $g_{z}^{R} = 4.5$ , and $t_{x} = t_{y} = t_{z} = 0.01 t$ .
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