4. STM Simulations - Tersoff-Hamann
To describe scanning tunneling microscopy (STM) at low bias and weak tip-sample coupling, the RESCU code adopts the Tersoff-Hamann (TH) formalism.
In the TH picture, the metallic tip is modeled by an s-wave state at the apex and the tunneling current at bias V is proportional to the local density of states (LDOS) of the system at the tip position, integrated from the Fermi level \(E_{F}\) to \(E_{F}+eV\) [Bar61_, TH83_].
Consequently, the differential conductance \(dI/dV\) approximates the LDOS evaluated at \(E_{F}+eV\) [TH85]. This provides a fast and reliable route to generate constant-height and constant-current topographies and bias-resolved STS spectra.
The TH approximation is accurate for small biases, tunneling-regime distances, and a featureless (s-like) tip apex. Within its validity window, RESCU + TH offers an efficient and widely used bridge between first-principles electronic structure and experimentally accessible STM/STS observables.