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arXiv:2606.14487

Spin-orbit coupling by design in quantum state engineering of atomically defined quantum dots

Hermann Osterhage, Julian H. Strik, Ivan Ado, Anna M. H. Krieg, Daniel Wegner, Mikhail Titov, Alexander A. Khajetoorians

cond-mat.mes-hallquant-phSubmitted Jun 12, 2026• Announced Jun 15, 2026
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Abstract

Tuning spin-orbit coupling is essential in controlling both spin and charge in confined semiconductor nanostructures, yet it is rarely a truly controllable parameter. Here, we show control over the spin-orbit Hamiltonian in quantum dots and the resulting quantum states by tailoring the confinement potential with atomic-scale precision. Using scanning tunnelling microscopy and spectroscopy, we pattern individual Cs ions into designer quantum dot structures on the surface of indium antimonide, in which electrons from a two-dimensional electron gas are confined with chosen in-plane electric-field gradients. We then quantify the atomic level structure, both spatially resolving the orbital character of the electronic states and their magnetic-field evolution. We demonstrate that the level structure, including the induced zero-field splitting, can be tailored by the designed geometry of the local electric fields. These effects can be described using a Hamiltonian that allows consistent treatment of the confinement-induced spin-orbit coupling beyond the conventional Bychkov-Rashba description. This Hamiltonian is derived from a multiband k.p model and takes the energy dependence of the relevant physical parameters into account. Such precise control of spin-orbit coupling in semiconductor quantum dots is relevant to quantum and spintronic technologies.

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Tuning spin-orbit coupling is essential in controlling both spin and charge in confined semiconductor nanostructures, yet it is rarely a truly controllable parameter. Here, we show control over the spin-orbit Hamiltonian in quantum dots and the resulting quantum states by tailoring the confinement potential with atomic-scale precision. Using scanning tunnelling microscopy and spectroscopy, we pattern individual Cs ions into designer quantum dot structures on the surface of indium antimonide, in which electrons from a two-dimensional electron gas are confined with chosen in-plane electric-field gradients. We then quantify the atomic level structure, both spatially resolving the orbital character of the electronic states and their magnetic-field evolution. We demonstrate that the level structure, including the induced zero-field splitting, can be tailored by the designed geometry of the local electric fields. These effects can be described using a Hamiltonian that allows consistent treatment of the confinement-induced spin-orbit coupling beyond the conventional Bychkov-Rashba description. This Hamiltonian is derived from a multiband k.p model and takes the energy dependence of the relevant physical parameters into account. Such precise control of spin-orbit coupling in semiconductor quantum dots is relevant to quantum and spintronic technologies.
In the last years, the electron spin in quantum dots has become a most promising candidate for the realization of qubits, the basic element for quantum computation. In quantum dot spin qubits the exchange interaction implements a fundamental two qubit gate, which originates in the Coulomb interaction and the Pauli principle. Compared to single qubit gates, the exchange based gates are much faster and easier to control locally, motivating the solely exchange energy based quantum computation. The control is based on the exponential sensitivity of the exchange energy on the interparticle distance. Manipulation then can proceed, for example, shifting the single particle states electrically or compressing them magnetically. The practical manipulation schemes require quantitative knowledge of the exchange energy. The spin-orbit interaction plays an important role in this nano-system. Indeed the usual exchange interaction changes its magnitude, while a new term, called anisotropic exchange, appears. In this thesis we propose an accurate effective spin Hamiltonian for modeling spin-orbit-induced spin dynamics in the presence of the magnetic field. We have also performed numerically exact calculations of the isotropic and anisotropic exchange coupling in realistic two-electron GaAs coupled quantum dots in the presence of both Dresselhaus and Bychkov-Rashba spin-orbit interactions. The numerics allow us to establish the goodness of our model and to see the limits of previous statements. Furthermore we find that in zero magnetic field the second-order spin-orbit effects are absent at all interdot couplings.
A nanodevice capable of separating spins of two electrons confined in a quantum dot formed in a gated semiconductor nanowire is proposed. Two electrons confined initially in a single quantum dot in the singlet state are transformed into the system of two electrons confined in two spatially separated quantum dots with opposite spins. In order to separate the electrons' spins we exploit transitions between the singlet and the triplet state, which are induced by resonantly oscillating Rashba spin-orbit coupling strength. The proposed device is all electrically controlled and the electron spin separation can be realized within tens of picoseconds. The results are supported by solving numerically the quasi-one-dimensional time-dependent Schroedinger equation for two electrons, where the electron-electron correlations are taken into account in the exact manner.
Matter at the atomic-scale is inherently governed by the laws of quantum mechanics. This makes charges and spins confined to individual atoms—and interactions among them—an invaluable resource for fundamental research and quantum technologies alike. However, harnessing the inherent ‘quantumness’ of atomic-scale objects requires that they can be precisely engineered and addressed at the individual atomic level. Since its invention in the 1980s, scanning tunnelling microscopy (STM) has repeatedly demonstrated the unrivalled ability to not only resolve but manipulate matter at atomic length scales. Over the past decades, this has enabled the design and investigation of bottom-up tailored nanostructures as reliable and reproducible platforms to study designer quantum physics and chemistry, band topology, and collective phenomena. The vast range of STM-based techniques and modes of operation, as well as their combination with electromagnetic fields from the infrared to microwave spectral range, has even allowed for the precise control of individual charge and spin degrees of freedom. This roadmap reviews the most recent developments in the field of atomically-engineered quantum platforms and explores their potential in future fundamental research and quantum technologies.
Matter at the atomic-scale is inherently governed by the laws of quantum mechanics. This makes charges and spins confined to individual atoms—and interactions among them—an invaluable resource for fundamental research and quantum technologies alike. However, harnessing the inherent ‘quantumness’ of atomic-scale objects requires that they can be precisely engineered and addressed at the individual atomic level. Since its invention in the 1980s, scanning tunnelling microscopy (STM) has repeatedly demonstrated the unrivalled ability to not only resolve but manipulate matter at atomic length scales. Over the past decades, this has enabled the design and investigation of bottom-up tailored nanostructures as reliable and reproducible platforms to study designer quantum physics and chemistry, band topology, and collective phenomena. The vast range of STM-based techniques and modes of operation, as well as their combination with electromagnetic fields from the infrared to microwave spectral range, has even allowed for the precise control of individual charge and spin degrees of freedom. This roadmap reviews the most recent developments in the field of atomically-engineered quantum platforms and explores their potential in future fundamental research and quantum technologies.
Individual spin defects in solids are promising building blocks for quantum technologies, but their deterministic creation, individual addressability, and operation near surfaces remain major challenges. Two-dimensional materials provide an attractive alternative, as their single-layer thickness enables direct atomic-scale access to defect states. Here, we demonstrate single-spin control of solid-state defects in a two-dimensional semiconductor by a combination of scanning tunneling microscopy and electron spin resonance. We create and manipulate individual sulfur vacancies and carbon substitution defects in monolayer molybdenum disulfide and characterize their spin dynamics, including coherent control, at the single-defect level. Using atomic manipulation, we further engineer and probe spin-spin interactions between defect pairs. Our results demonstrate deterministic creation, addressability, coherent manipulation, and controlled coupling of individual spin defects within a single experimental platform. This establishes atomically engineered spin defects in two-dimensional semiconductors as a versatile class of controllable solid-state quantum systems and opens a route towards tailored quantum sensing experiments.
We have studied theoretically the possibility of ultra-fast manipulation of a single electron spin in 2D semiconductor quantum dots, by means of high-frequency time-dependent electric fields. The electron spin degree of freedom is excited through spin-orbit coupling, and the procedure may be enhanced by the presence of a static magnetic field. We use quantum optimal control theory to tailor the temporal profile of the electric field in order to achieve the most effective manipulation. The scheme predicts significant control over spin operations in times of the order of picoseconds -- an ultrafast time scale that permits to avoid the effects of decoherence if this scheme is to be used as a tool for quantum information processing.