Energy-resolved tip-orbital fingerprint in scanning tunneling spectroscopy based on the revised Chen's derivative rule

The revised Chen's derivative rule for electron tunneling is implemented to enable computationally efficient first-principles-based calculations of the differential conductance dI/dV for scanning tunneling spectroscopy (STS) simulations. The probing tip is included through a single tip apex atom, and its electronic structure can be modeled as a linear combination of electron orbitals of various symmetries, or can be directly transferred from first-principles electronic structure calculations. By taking pristine and boron- or nitrogen-doped graphene sheets as sample surfaces, the reliability of our implementation is demonstrated by comparing its results to those obtained by the Tersoff-Hamann and Bardeen's electron tunneling models. It is highlighted that the energy-resolved direct and interference contributions to dI/dV arising from the tip's electron orbitals result in a fingerprint of the particular combined surface-tip system. The significant difference between the electron acceptor boron and donor nitrogen dopants in graphene is reflected in their dI/dV fingerprints. The presented theoretical method allows for an unprecedented physical understanding of the electron tunneling process in terms of tip-orbital-resolved energy-dependent dI/dV maps, that is anticipated to be extremely useful for investigating the local electronic properties of novel material surfaces in the future.