Transfer Hamiltonian analytical theory of scanning tunneling spectroscopy

The transfer Hamiltonian approach to the scanning tunneling spectroscopy (STS) is extended in a twofold direction. First, a theory representing an extension to the case of arbitrary temperature and applied voltage of the work of Chen [Phys. Rev. B 42, 8841 (1990)] is developed. Within this framework analytical expressions of the tunneling current and its derivative can be obtained under rather general assumptions for the tip density of states. In particular, the situation of a general electronic structure of the tip states is considered. The calculation of theoretical $dI∕dV$ curves and conductivity maps, to be compared with experiments and numerical simulations, becomes possible and these results lead also to the best normalization procedure of the current derivative to obtain the desired physical information, namely, the sample local density of states, provided the electronic tip properties are known. Second, a general theoretical description in terms of the system spectral densities is derived, providing a generalization of the approach developed by Feuchtwang and Cutler [Phys. Scr. 38, 252 (1988)]. We believe that with these achievements the forecast of STS theory gets significantly closer to the experimental results.