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Physical Review Applied

Electrical spin manipulation in SrTiO3 / LaAlO3 double quantum dots

B. Szafran, P. Wójcik, M. Zegrodnik, M. P. Nowak, R. Citro

Published Oct 4, 2024• 3 citations
Publisher

Abstract

The spin dynamics in two electron double quantum dots embedded in a two-dimensional electron gas at the interface between ${\mathrm{Sr}\mathrm{Ti}\mathrm{O}}_{3}$ and ${\mathrm{La}\mathrm{Al}\mathrm{O}}_{3}$ is studied by an exact numerical solution of the time-dependent Schr\"odinger equation in the context of the electric-dipole-spin-resonance experiment. On the basis of the three-band model of $3d$ electrons localized at $\mathrm{Ti}$ ions on the square lattice, we analyze in detail the singlet-triplet transition induced by the ac electric field, in the magnetic field range close to the avoided crossing that appears as a result of the spin-orbit coupling. For symmetric double quantum dots the single-photon spin-flip transition is prohibited due to the parity symmetry, and the transition can occur only by the higher-order two-photon processes. For a weakly asymmetric system, when the first-order singlet-triplet transitions are released due to the parity symmetry breaking, the spin-flip transition has a character of the Rabi oscillations for a low electric field amplitude. As the amplitude is increased, the frequency of the transition is blueshifted (redshifted) for the magnetic field below (above) the single-triplet avoided crossing. For a sufficiently high magnetic field and high ac-field amplitude, the electric field drives the system across the avoided crossing, inducing the spin flip by the Landau-Zener-Stueckelberg-Majorana effect. Finally, the optimization of the geometrical parameters of the system with respect to the time of spin flip of its fidelity is also presented.

DOI
10.1103/physrevapplied.22.044012

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The spin dynamics in two electron double quantum dots embedded in a two-dimensional electron gas at the interface between SrTiO3{\mathrm{Sr}\mathrm{Ti}\mathrm{O}}_{3}SrTiO3​ and LaAlO3{\mathrm{La}\mathrm{Al}\mathrm{O}}_{3}LaAlO3​ is studied by an exact numerical solution of the time-dependent Schr"odinger equation in the context of the electric-dipole-spin-resonance experiment. On the basis of the three-band model of 3d3d3d electrons localized at Ti\mathrm{Ti}Ti ions on the square lattice, we analyze in detail the singlet-triplet transition induced by the ac electric field, in the magnetic field range close to the avoided crossing that appears as a result of the spin-orbit coupling. For symmetric double quantum dots the single-photon spin-flip transition is prohibited due to the parity symmetry, and the transition can occur only by the higher-order two-photon processes. For a weakly asymmetric system, when the first-order singlet-triplet transitions are released due to the parity symmetry breaking, the spin-flip transition has a character of the Rabi oscillations for a low electric field amplitude. As the amplitude is increased, the frequency of the transition is blueshifted (redshifted) for the magnetic field below (above) the single-triplet avoided crossing. For a sufficiently high magnetic field and high ac-field amplitude, the electric field drives the system across the avoided crossing, inducing the spin flip by the Landau-Zener-Stueckelberg-Majorana effect. Finally, the optimization of the geometrical parameters of the system with respect to the time of spin flip of its fidelity is also presented.
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The spin dynamics in two electron double quantum dots embedded in two dimensional electron gas at the interface between SrTiO3_33​ and LaAlO3_33​ is studied by an exact numerical solution of the time-dependent Schrödinger equation, in the context of the electric dipole spin resonance experiment. Based on the three band model of 3d3d3d-electrons localized at Ti ions on the square lattice we analyze in details the singlet-triplet transition induced by the AC electric field, in the magnetic field range close to the avoided crossing which appears as a result of the spin-orbit coupling. Our calculations show that for symmetric double quantum dots the single photon spin-flip transitions is prohibited due to the parity symmetry and the transition can occur only by the higher order two-photon processes. For a weakly asymmetric system, when the first order singlet-triplet transitions are released due to the parity symmetry breaking, the spin-flip transition has a character of the Rabi oscillations for a low electric field amplitude. As the amplitude is increased the frequency of the transition is blueshifted (redshifted) for the magnetic field below (above) the single-triplet avoided crossing. Interestingly, for a sufficiently high magnetic field and high AC field amplitude the electric field drives the system across the avoided crossing inducing the spin-flip by the Landau-Zener-Stueckelberg-Majorana transitions with 100\% spin flip probability for a slow sweep. Finally, the optimization of the geometrical parameters of the system with respect to the time of spin-flip of its fidelity is also presented.
We investigate the energy spectrum of a single- and two-electron quantum dot (QD) embedded in two-dimensional electron gas at the interface between SrTiO3{\mathrm{SrTiO}}_{3}SrTiO3​ and LaAlO3{\mathrm{LaAlO}}_{3}LaAlO3​, in the presence of the external magnetic field. For this purpose, the three-band model of 3d3d3d electrons defined on the square lattice of Ti ions was utilized. We demonstrate that, for the weak parabolic confinement potential, the low-energy spectrum is sufficiently well described by the effective Hamiltonian reduced to the one dxy{d}_{xy}dxy​ orbital with the spin-orbit interaction originating from the coupling to the dxz{d}_{xz}dxz​ and dyz{d}_{yz}dyz​ bands. This is not the case for stronger confinement where contribution of the states related to the dxz/yz{d}_{xz/yz}dxz/yz​ orbital is relevant. Based on the time-dependent calculations, we discuss in detail the manipulation of the electron spin in a QD by external AC voltages, in the context of the electric dipole spin resonance. The allowed and forbidden transitions are discussed in detail with respect to the parity selection rule. Our calculations show that, for a single-electron QD, the spin flip in the ground state has the character of a Rabi resonance, while for two electrons, the singlet-triplet transition is forbidden by the parity symmetry. For the two-electron QD, we demonstrate that the spin-flip transition can still be accomplished via a second-order, two-photon process that has a two-state Rabi character for low AC field amplitude. The violation of the parity symmetry on the spin-flip transitions is also analyzed.
The spin-orbit interaction permits to control the state of a spin qubit via electric fields. For holes it is particularly strong, allowing for fast all electrical qubit manipulation, and yet an in-depth understanding of this interaction in hole systems is missing. Here we investigate, experimentally and theoretically, the effect of the cubic Rashba spin-orbit interaction on the mixing of the spin states by studying singlet-triplet oscillations in a planar Ge hole double quantum dot. Landau-Zener sweeps at different magnetic field directions allow us to disentangle the effects of the spin-orbit induced spin-flip term from those caused by strongly site-dependent and anisotropic quantum dot g tensors. Our work, therefore, provides new insights into the hole spin-orbit interaction, necessary for optimizing future qubit experiments.
Single-spin state evolution induced by the Landau-Zener-St\"uckelberg-Majorana (LZSM) interference in a Zeeman-spit four-level system in a periodically driven double quantum dot is studied theoretically by the Floquet stroboscopic method. An interplay between spin-conserving and spin-flip tunneling processes with the electric dipole spin resonance (EDSR) that is induced in an individual dot and enhanced by the LZSM multiple level crossings with the neighboring quantum dot is investigated as a function of the microwave (MW) frequency, driving amplitude, interdot detuning, and magnetic field. A number of special points in the parameter space are identified, out of which all three features are merged. Under this triple-crossing resonance condition, the interdot tunneling is combined with a fast spin evolution in each dot at the EDSR frequency. Harmonics of the EDSR are revealed in the spin-dependent tunneling maps versus variable magnetic field and MW frequency. The results are applicable for both electron and hole systems with strong spin-orbit interaction and may be useful for developing new time-efficient schemes of the spin control and readout in qubit devices.
Bartlomiej Szafran AGH University of Science and Technology, Kraków(Poland)Driven spin transitions in quantum dots at the interface between SrTiO3and LaAlO3Abstract:The talk focuses on the results of the tight-binding modeling of single-and two-electron statesin a quantum dot and a double quantum dot and on the simulations of the spin transitionsdriven by periodic electric field. The symmetry of the states in the context of harmonic andsubharmonic transitions is discussed. The talk reports on the optimization of the drivensinglet-triplet transitionsby the asymmetry of the double quantum dot. Rabi vs Landau-Zenertransition regimes are discussed.
Progress in the fabrication of nanoscale transition-metal-oxide heterostructures makes these platforms promising candidates for the realization of spin qubits, mainly due to the ddd-character of their electronic structures, which could potentially result in a reduction of hyperfine interactions and spin decoherence. Here, we present a systematic study of spin control within the SWAP operation in double quantum dots embedded in a two-dimensional electron gas at the LaAlO3_33​/SrTiO3_33​ interface. Our analysis starts with a study of single-electron spin dynamics, focusing on the influence of spin-orbit and interorbital coupling on the spin evolution. In this case, our findings are supported by semiclassical calculations based on the Bloch equations, which show good agreement with full quantum mechanical simulations. We then simulate the SWAP operation by analyzing the crossover between two regimes: (i) large quantum dots, where the electronic structure is dominated by the dxyd_{xy}dxy​ orbitals and the spin dynamics is affected primarily by Rashba-type spin-orbit interaction; and (ii) small quantum dots, where higher-energy orbitals dxz/yzd_{xz/yz}dxz/yz​ contribute to the electronic structure, leading to a significant reduction in the SWAP fidelity. In the first regime, particularly relevant from the application point of view, we analyze in detail the anisotropy of the SWAP operation induced by the spin-orbit coupling.