Orbital dependent electron tunneling within the atom superposition approach: Theory and application to W(110)

We introduce an orbital dependent electron tunneling model and implement it within the atom superposition approach for simulating scanning tunneling microscopy (STM) and spectroscopy (STS). Applying our method, we analyze the convergence and the orbital contributions to the tunneling current and the corrugation of constant current STM images above the W(110) surface. In accordance with a previous study [Heinze et al., Phys. Rev. B 58, 16432 (1998)], we find atomic contrast reversal depending on the bias voltage. Additionally, we analyze this effect depending on the tip-sample distance using different tip models, and find two qualitatively different behaviors based on the tip orbital composition. As an explanation, we highlight the role of the real space shape of the orbitals involved in the tunneling. STM images calculated by our model agree well with Tersoff-Hamann and Bardeen results. The computational efficiency of our model is remarkable as the k-point samplings of the surface and tip Brillouin zones do not affect the computation time, in contrast to the Bardeen method.

💡 Research Summary

The paper presents a new theoretical framework for simulating scanning tunneling microscopy (STM) and spectroscopy (STS) that explicitly incorporates orbital‑dependent electron tunneling within the atom‑superposition approach. Traditional atom‑superposition methods sum contributions from surface atoms without distinguishing between the different atomic orbitals that dominate tunneling. Here, the authors derive a tunneling current expression in which each term is indexed by a surface atom i and by the specific orbitals α (on the sample) and β (on the tip):

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