Shockley surface states (SS) have attracted much attention due to their role in various physical phenomena occurring at surfaces. It is also clear from experiments that they can play an important role in electron transport. However, accurate incorporation of surface states in $textit{ab initio}$ quantum transport simulations remains still an unresolved problem. Here we go beyond the state-of-the-art non-equilibrium Greens function formalism through the evaluation of the self-energy in real-space, enabling electron transport without using artificial periodic in-plane conditions. We demonstrate the method on three representative examples based on Au(111): a clean surface, a metallic nanocontact, and a single-molecule junction. We show that SS can contribute more than 30% of the electron transport near the Fermi energy. A significant and robust transmission drop is observed at the SS band edge due to quantum interference in both metallic and molecular junctions, in good agreement with experimental measurements. The origin of this interference phenomenon is attributed to the coupling between bulk and SS transport channels and it is reproduced and understood by tight-binding model. Furthermore, our method predicts much better quantized conductance for metallic nanocontacts.
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