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arXiv:2606.01938

Magnetic control of electron scattering in silicene quantum dots

Mohamed El Azar, Elmustapha Feddi, Pablo Díaz, David Laroze, Ahmed Jellal

cond-mat.mes-hallquant-phSubmitted Jun 1, 2026• Announced Jun 2, 2026
arXivHTMLPDF

Abstract

The Klein tunnel effect phenomenon makes it impossible to permanently confine charge carriers in massless nanostructures. However, applying a constant magnetic field allows these electrons to be temporarily localized, thus forming quasi-bound states. In this study, we analyze the mechanism of electron diffusion through a silicene quantum dot (SQD) subjected to a perpendicular magnetic field. To enhance spatial localization, we exploit the spin-orbit coupling (SOC) specific to silicene, which generates a natural energy gap by acting as an effective mass. We first derive the solutions to the Dirac equation at low energy. Subsequently, by imposing the continuity conditions at the SQD interfaces, we obtain exact expressions for the diffusion coefficients. These results are then used to map the scattering efficiency together with the spatial distributions of probability and current densities. Our simulations demonstrate that the presence of this intrinsic gap significantly enhances electron trapping at the center of the SQD. Finally, we prove that the interplay between the external field and SOC breaks spin symmetry, thereby enabling robust and spin-selective confinement.

Journal reference
Annals of Physics 492 (2026) 170543
DOI
10.1016/j.aop.2026.170543
Comments
12 pages, 7 figures

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The Klein tunnel effect phenomenon makes it impossible to permanently confine charge carriers in massless nanostructures. However, applying a constant magnetic field allows these electrons to be temporarily localized, thus forming quasi-bound states. In this study, we analyze the mechanism of electron diffusion through a silicene quantum dot (SQD) subjected to a perpendicular magnetic field. To enhance spatial localization, we exploit the spin-orbit coupling (SOC) specific to silicene, which generates a natural energy gap by acting as an effective mass. We first derive the solutions to the Dirac equation at low energy. Subsequently, by imposing the continuity conditions at the SQD interfaces, we obtain exact expressions for the diffusion coefficients. These results are then used to map the scattering efficiency together with the spatial distributions of probability and current densities. Our simulations demonstrate that the presence of this intrinsic gap significantly enhances electron trapping at the center of the SQD. Finally, we prove that the interplay between the external field and SOC breaks spin symmetry, thereby enabling robust and spin-selective confinement.
Confinement in a magnetically induced WSe2_22​ quantum dots
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While bulk silicon has long been understood to exhibit relatively weak spin-orbit coupling (SOC), confinement of electrons to quantum dots (QDs) at a silicon heterointerface results in significantly larger SOC. This is a concern for electron spin qubit performance, as intravalley and intervalley SOC can significantly perturb the operation of electron spin qubits. While these interactions can be harnessed to drive coherent rotations in a singlet-triplet qubit, coupling to low-lying excited valley states can lead to undesirable spin relaxation when valley splitting is on resonance with the Zeeman energy. In this work, we measure the angular dependence of the interfacial spin-orbit interaction as a function of the direction and magnitude of an applied external magnetic field in SiMOS and Si/SiGe heterostructures, two common material platforms for silicon spin qubits. We construct a physical model that accurately infers intra- and inter-valley SOC physics from fits to the data, allowing for a direct comparison between these two material systems. For the devices measured we find that, while the ggg-factor differences are comparable, the SiMOS QDs exhibit an order of magnitude larger spin-valley coupling than for Si/SiGe. Moreover, we find that the angular dependence of the spin-valley coupling is similar for both devices, with similar magnetic field orientations minimizing the spin-valley coupling. Our work points towards operational schemes for optimizing spin-valley coupling to avoid or exploit this mechanism for qubit operation.
Abstract We use quantum perturbation theory with the exact general solutions of the perturbed equations to investigate a single electron confined in a gated nanowire quantum dot (NQD) with arbitrarily strong spin–orbit coupling (SOC) and weak static magnetic field. Treating the weak field as a perturbation, we obtain the maximal spin-motion entangled kitten states. From the double-boundedness and self-consistence conditions of the general bound-state solutions we uncovered two corrected energies and the explicit dependence of the spin–orbit state phase on the orientation of the applied magnetic field and the SOC parameters. The two-level states correspond to a spin–orbit qubit with the level splitting being much less than the unperturbed level-difference. We demonstrate the higher stability of the ground states and the SOC strength-related decoherence-averse effect, meaning the robustness of the qubit against external fluctuations (or decoherence). We suggest an alternative scheme to perform the qubit manipulation, simply by adjusting the orientation angle of magnetic field to produce the quantized phase jumps. Such an adjustment can lead to the SOC phase-related spin flipping of the state vectors and the position exchanging of the probability-density wavepackets, which can be explained as the quantized change of the qubit spin axis. The results can be applied to a weakly coupled array of NQDs for coherently encoding the robust spin–orbit qubits, and could be extended to a cold-atomic system with the laser-induced SOC.
We present a theoretical study of electron tunneling through a magnetic barrier in 8-Pmmn borophene, created by depositing two ferromagnetic strips on the borophene sheet. Using a low-energy effective Hamiltonian that captures the anisotropic Dirac spectrum, we solve the Dirac equation in three regions and impose wave-function continuity at the interfaces. From the resulting spinor solutions, we compute current densities and determine transmission and reflection probabilities as functions of incident energy, angle, and barrier parameters. The transmission exhibits strong anisotropy due to the tilted Dirac cones, with pronounced suppression for specific incident directions, suggesting directional filtering of carriers. We further calculate the conductance using the Landauer-Büttiker formalism, revealing that both magnetic strength and barrier width can tune the charge transport properties. The results demonstrate that engineered magnetic barriers in 8-Pmmn borophene enable precise control over electron flow, offering a platform for anisotropic transport control and tunable quantum devices. The interplay between the intrinsic anisotropy of borophene and external magnetic barriers provides rich opportunities to manipulate Dirac fermions in two-dimensional systems.