Scanning tunneling microscopy (STM) has been utilized
to realize
the precise measurement and control of local spin states. Experiments
have demonstrated that when a nickelocene (Nc) molecule is attached
to the apex of an STM tip, the dI/dV spectra exhibit a sharp or a smooth transition when the tip is displaced
toward the substrate. However, what leads to the two distinct types
of transitions remains unclear, and more intriguingly, the physical
origin of the abrupt change in the line shape of dI/dV spectra remains unclear. To clarify these intriguing
issues, we perform first-principles-based simulations on the STM tip
control process for the Cu tip/Nc/Cu(100) junction. In particular,
we find that the suddenly enhanced hybridization between the d orbitals
on the Ni ion and the metallic bands in the substrate leads to Kondo
correlation overwhelming spin excitation, which is the main cause
of the sharp transition in the dI/dV spectra observed experimentally.
Recent technological advancement in scanning tunneling microscope has enabled the measurement of spin-field and spin-spin interactions in single atomic or molecular junctions with an unprecedentedly high resolution. Theoretically, although the fermionic hierarchical equations of motion (HEOM) method has been widely applied to investigate the strongly correlated Kondo states in these junctions, the existence of low-energy spin excitations presents new challenges to numerical simulations. These include the quest for a more accurate and efficient decomposition for the non-Markovian memory of low-temperature environments, and a more careful handling of errors caused by the truncation of the hierarchy. In this work, we propose several new algorithms, which significantly enhance the performance of the HEOM method, as exemplified by the calculations on systems involving various types of low-energy spin excitations. Being able to characterize both the Kondo effect and spin excitation accurately, the HEOM method offers a sophisticated and versatile theoretical tool which is valuable for the understanding and even prediction of the fascinating quantum phenomena explored in cutting-edge experiments.
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