Nonlocality of the exchange interaction probed by scanning tunneling spectroscopy

Abstract

The energy states of the tip induced quantum dot are investigated in a magnetic field as a function of the tip position with respect to the surface. To study the influence of potential perturbations on the exchange interaction in the quantum dot, emphasis is given on the Landau and spin levels probed at positive bias. Mapping of the spatial dependence of the peak energies and comparison with the surface potential map-reconstructed from the analysis of scattering states around ionized dopants-reveals that the fluctuating surface potential acts as a local perturbation on the quantum dot states. In contrast, the spin splitting is influenced nonlocally by the surface potential, which directly evidences the nonlocal character of the exchange interaction.Quantum dots, often called artificial atoms, have been investigated extensively in the past, since their increased size with respect to atoms allows to study the influence of strong magnetic fields and correlation effects on the electronic structure of a system confined in all three dimensions. 1 The small electron density in the quantum dot favors the influence of electron-electron interactions. In particular, the nonlocal character of the exchange interaction leads to a complex correlation of the energy levels with potential perturbations always present in real systems.The aim of this Rapid Communication is to probe these correlations. We use the recently discovered tip induced quantum dot ͑QD͒, 2 introduced into a semiconductor surface by the tip of a scanning tunneling microscope ͑STM͒. The tip acts as a local gate movable over the surface and, by moving the QD probes different potential environments of the surface. Thus the potential fluctuations of the sample act as spatially varying perturbations on the confinement potential. The resulting exchange interaction is directly probed by measuring the spin splitting of the QD, i.e., we record dI/dV curves exhibiting spin split states in magnetic field. 3 A comparison of the resulting spatial map of the spin splitting with the surface potential map answers the question, if the exchange interaction reacts locally or nonlocally on potential perturbations. As expected, we find a nonlocal correlation, which, to our knowledge, is the first microscopic visualization of the nonlocal character of the exchange interaction.Besides this physical aspect, the study has also a technological aspect: the spin of a quantum dot has been proposed as a basic unit ͑qubit͒ in quantum computation. 4 The spin degree of freedom provides a reasonable coherence time and, importantly, the approach can be extended to a large number of qubits. 5 However, in contrast to atoms, quantum dots suffer from their imperfections in the confinement potential leading to slightly varying level schemes between nominally identical dots. 6 Hence, the influence of potential perturbations on the spin splitting has to be understood to realize controllable devices. This study is a first step in that direction, although we did not find a quantitative model to explain...

Scanning tunneling spectroscopy of a dilute two-dimensional electron system exhibiting Rashba spin splitting

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Poor electronic screening in lightly doped Mott insulators observed with scanning tunneling microscopy

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Valley Filtering in Spatial Maps of Coupling between Silicon Donors and Quantum Dots

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